Systems and methods for adaptive blind mode equalization

ABSTRACT

A blind mode adaptive equalizer system to recover the in general complex valued data symbols from the signal transmitted over time-varying dispersive wireless channels is disclosed comprising an adaptive communication receiver for the demodulation and detection of digitally modulated signals received over wireless communication channels exhibiting multipath and fading, the receiver comprising an RF front end, an RF to complex baseband converter, a band limiting matched filter, a channel gain normalizer, a blind mode adaptive equalizer with hierarchical structure, an initial data segment recovery circuit, a differential decoder, a complex baseband to data bit mapper, and an error correction code decoder and de-interleaver.

CROSS-REFERENCES TO RELATED APPLICATIONS

This divisional application claims priority from U.S. application Ser.No. 13/434,498, filed Mar. 29, 2012 incorporated by reference in itsentirety.

BACKGROUND

Broadband wireless systems are currently in a rapid evolutionary phasein terms of development of various technologies, development of variousapplications, deployment of various services and generation of manyimportant standards in the field. The increasing demand on variousservices justifies the need for the transmission of data on variouscommunication channels at the highest possible data rates. The multipathand fading characteristics of the wireless channels result in variousdistortions, the most important of those being the inter-symbolinterference (ISI) especially at relatively high data rates. Adaptiveequalizers are employed to mitigate the ISI introduced by the timevarying dispersive channels and possibly arising from other sources. Inone class of adaptive equalizers, a training sequence known to thereceiver is transmitted that is used by adaptive equalizer for adjustingthe equalizer parameter vector to a value that results in a relativelysmall residual ISI. After the training sequence, the data is transmittedduring which period the equalizer continues to adapt to slow channelvariations using decision directed method.

Among the various algorithms to adapt the equalizer parameter vector arethe recursive least squares (RLS) algorithm, weighted Kaman filter, LMSalgorithm, and the quantized state (QS) algorithm, the last one taughtby Kumar et. al. in “Adaptive Equalization Via Fast Quantized-StateMethods,” IEEE Transactions on Communications, Vol. COM-29, No. 10,October 1981. Kumar at. al. teach orthogonalization process to arrive atfast and computationally efficient identification algorithms in, “StateInverse and Decorrelated State Stochastic Approximation,” Automatica,Vol. 16, May 1980. The training approach, however, is not desirable inmany communication applications such as those involving video conferencetype of applications that will require a training sequence every time adifferent speaker talks. Moreover, the need for training sequenceresults in a significant reduction in capacity as for example, in GSMstandard, a very significant part of each frame is used for theequalizer training sequence. Also, if during the decision-directed modethe equalizer deviates significantly due to burst of noise orinterference, all the subsequent data will be erroneously received bythe receiver until the loss of equalization is detected and the trainingsequence is retransmitted and so on.

There are many other applications where the equalizers are applied as inantenna beam forming, adaptive antenna focusing of the antenna, radioastronomy, navigation, etc. For example, Kumar et. al. teach in Methodand Apparatus for Reducing Multipath Signal Error Using Deconvolution,U.S. Pat. No. 5,918,161, June 1999, an equalizer approach for a verydifferent problem of precise elimination of the multipath error in therange measurement in GPS receiver. In all of the various applications ofequalizers and due to various considerations such as the logistics andefficiency of systems, it has been of great interest to have theequalizer adapt without the need for a training sequence. Suchequalizers are the termed the “blind mode” equalizers.

Among some of the approaches to blind mode equalization are the Sato'salgorithm and Goddard's algorithm that are similar to the LMS and RLSalgorithms, respectively, except that these may not have any trainingperiod. Kumar, in “Convergence of A Decision-Directed AdaptiveEqualizer,” Proceedings of the 22nd IEEE Conference on Decision andControl, 1983, Vol. 22, teaches a technique wherein an intentional noisewith relatively high variance is injected into the decision-directedadaptive algorithm with the noise variance reduced as the convergenceprogressed and shows that the domain of convergence of the blind modeequalizer was considerably increased with the increase in the noisevariance at the start of the algorithm. The technique taught by Kumar isanalogous to the annealing in the steel process industry and in fact theterm simulated annealing was coined after the introduction by Kumar.Lambert et. al., teach the estimation of the channel impulse responsefrom the detected data in, “Forward/Inverse Blind Equalization,” 1995Conference Record of the 28th Asilomar Conference on Signals, Systemsand Computers, Vol. 2, 1995. Another blind mode equalization methodapplicable to the case where the modulated data symbols have a constantenvelope and known as constant modulus algorithm (CMA) taught by Goddardin “Self-recovering Equalization and Carrier Tracking in Two-DimensionalData Communication System,” IEEE Transactions on Communications, vol.28, No. 11, pp. 1867-1875, November, 1980, is based on minimization ofthe difference between the magnitude square of the estimate of theestimate of the data symbol and a constant that may be selected to be 1.

The prior blind mode equalizers have a relatively long convergenceperiod and are not universally applicable in terms of the channels to beequalized and in some cases methods such as the one based on polyspectraanalysis are computationally very expensive. The CMA method is limitedto only constant envelope modulation schemes such as M-phase shiftkeying (MPSK) and thus are not applicable to modulation schemes such asM-quadrature amplitude modulation (MQAM) and M-amplitude shift keying(MASK) modulation that are extensively used in wireless communicationsystems due to their desirable characteristics. Tsuie et. al. in,Selective Slicing Equalizer, Pub. No. US 2008/0260017 A1, Oct. 23, 2008,taught a selective slicing equalizer wherein in a decision feedbackequalizer configuration, the input to the feedback path may be selectedeither from the combiner output or the output of the slicer dependingupon the combiner output.

The prior blind mode equalization techniques may involve local minima towhich the algorithm may converge resulting in high residual ISI. Thus itis desirable to have blind mode adaptive equalizers that are robust andnot converging to any local minima, have wide applicability without, forexample, restriction of constant modulus signals, are relatively fast inconvergence, and are computationally efficient. The equalizers of thisinvention possess these and various other benefits.

Various embodiments described herein are directed to methods and systemsfor blind mode adaptive equalizer system to recover the in generalcomplex valued data symbols from a signal transmitted over time-varyingdispersive wireless channels. For example, various embodiments mayutilize an architecture comprised of a channel gain normalizer comprisedof a channel signal power estimator, a channel gain estimator and aparameter α estimator for providing nearly constant average power outputand for adjusting the dominant tap of the normalized channel to close to1, a blind mode equalizer with hierarchical structure (BMAEHS) comprisedof a level 1 adaptive system and a level 2 adaptive system for theequalization of the normalized channel output, and an initial datarecovery for recovery of the data symbols received during the initialconvergence period of the BMAEHS and pre appending the recovered symbolsto the output of the BMAEHS providing a continuous stream of all theequalized symbols.

The level 1 adaptive system of the BMAEHS is further comprised of anequalizer filter providing the linear estimate of the data symbol, thedecision device providing the detected data symbol, an adaptation blockgenerating the equalizer parameter vector on the basis of a firstcorrection signal generated within the adaptation block and a secondcorrection signal inputted from the level 2 adaptive system. The cascadeof the equalizer filter and the decision device is referred to as theequalizer. The first correction vector is based on the error between theinput and output of the decision device. However, in the blind mode ofadaptation, the first error may converge to a relatively small valueresulting in a false convergence or convergence to one of the localminima that are implicitly present due to the nature of the manner ofgeneration of the first error. To eliminate this possibility, the level2 adaptive system estimates a modeling error incurred by the equalizer.The modeling error is generated by first obtaining an independentestimate of the channel impulse response based on the output of thedecision device and the channel output and determining the modelingerror as the deviation of the impulse response of the composite systemcomprised of the equalizer filter and the estimate of the channelimpulse response from the ideal impulse comprised of all but one of itselements equal to 0. In case the equalizer tends to converge to a falseminimum, the magnitude of the modeling error gets large and the level 2adaptive system generates the second correction signal to keep themodeling error small and thereby avoiding convergence to a false orlocal minimum.

In the invented architecture, the channel gain estimator is to normalizethe output of the channel so as to match the level of the normalizedsignal with the levels of the slicers present in the decision device,thereby resulting in increased convergence rate during the initialconvergence phase of the algorithm. This is particularly important whenthe modulated signal contains at least part of the information encodedin the amplitude of the signal as, for example, is the case with theMQAM and MASK modulation schemes.

In another one of the various architectures of the invention for blindmode adaptive equalizer system, the BMAEHS is additionally comprised ofan orthogonalizer, wherein the two correction signals generated in level1 and level 2 adaptive systems are first normalized to have an equalmean squared norms and wherein the orthogonalizer provides a compositeorthogonalized correction signal vector to the equalizer. The process oforthogonalization results in introducing certain independence among thesequence of correction signal vectors. The orthogonalization may resultin fast convergence speeds in blind mode similar to those in theequalizers with training sequence.

In another one of the various architectures of the invention for blindmode adaptive equalizer system, the BMAEHS is replaced by a cascade ofmultiple equalizer stages with multiplicity m greater than 1 and witheach equalizer stage selected to be one of the BMAEHS or the simplerblind mode adaptive equalizer (BMAE). In the architecture, the input tothe ith equalizer stage is the linear estimate of data symbol generatedby the (i−1)th equalizer stage, and the detected data symbol from the(i−1)th equalizer stage provides the training sequence to the ithequalizer stage during the initial convergence period of the ithequalizer stage for i=2, . . . , m. In one of the embodiments of thearchitecture, m=2, with the first equalizer stage selected to be aBMAEHS and the second equalizer stage selected to be a BMAE. In thecascaded architecture, the BMAEHS ensures convergence bringing theresidual ISI to a relatively small error such that the next equalizerstage may employ a relatively simple LMS algorithm, for example. Theequivalent length of the cascade equalizer is the sum of the lengths ofthe m stages, and the mean squared error in the estimation of the datasymbol depends upon the total length of the equalizer, the cascadedarchitecture has the advantage or reduced computational requirementswithout a significant loss in convergence speed, as the computationalrequirement may vary more than linearly with the length of theequalizer,

Various architectures of the invention use a linear equalizer or adecision feedback equalizer in the level 1 adaptive system. In one ofthe various architectures of the invention, FFT implementation is usedfor the generation of the second correction signal resulting in afurther significant reduction in the computational requirements.

In various embodiments of the invention, an adaptive communicationreceiver for the demodulation and detection of digitally modulatedsignals received over wireless communication channels exhibitingmultipath and fading is described with the receiver comprised of an RFfront end, an RF to complex baseband converter, a band limiting matchedfilter, a channel gain normalizer, a blind mode adaptive equalizer withhierarchical structure, an initial data segment recovery circuit, adifferential decoder, a complex baseband to data bit mapper, and anerror correction code decoder and de-interleaver providing theinformation data at the output of the receiver without the requirementsof any training sequence.

The differential decoder in the adaptive receiver performs the functionthat is inverse to that of the encoder in the transmitter. Thedifferential encoder is for providing protection against phase ambiguitywith the number of phase ambiguities equal to the order of rotationalsymmetry of the signal constellation of the baseband symbols. The phaseambiguities may be introduced due to the blind mode of the equalization.The number of phase ambiguities for the MQAM signal is 4 for any M equalto N2 with N equal to any integer power of 2, for example M=16 or 64.The architecture for the differential encoder is comprised of a phasethreshold device for providing the reference phase for the sector towhich the baseband symbol belongs, a differential phase encoder, anadder to modify the output of the differential phase encoder by adifference phase, a complex exponential function block, and a multiplierto modulate the amplitude of the baseband symbol onto the output of thecomplex exponential function block, and applies to various modulationschemes. The architecture presented for the decoder is similar to thatof the differential encoder and is for performing the function that isinverse to that of the encoder.

In various embodiments of the invention, an adaptive beam former systemis described with the system comprised of an antenna array, a bank of RFfront ends receiving signals from the antenna array elements and a bankof RF to baseband converters with their outputs inputted to the adaptivedigital beam former that is further comprised of an adaptive combiner, acombiner gain normalizer, a decision device, and a multilevel adaptationblock for receiving data symbols transmitted form a source in a blindmode without the need for any training sequence and without therestriction of a constant modulus on the transmitted data.

BRIEF DESCRIPTION OF THE DRAWINGS

Various embodiments of the present invention are described here by wayof example in conjunction with the following figures, wherein:

FIG. 1 shows a block diagram of one embodiments of blind mode adaptiveequalizer system.

FIG. 2 shows one embodiment of the digital communication system withblind mode adaptive equalizer system.

FIG. 3A shows a block diagram one embodiment of differential encoder.

FIG. 3B shows the signal constellation diagram of 16QAM signal.

FIG. 4 shows a block diagram of one embodiment of differential decoder.

FIG. 5 shows a block diagram of one embodiment of channel gainnormalizer.

FIG. 6 shows a block diagram of one embodiment of blind mode adaptiveequalizer with hierarchical structure (BMAEHS) with linear equalizer.

FIG. 7 shows a block diagram of one embodiment of channel estimator.

FIG. 8 shows a block diagram of one embodiment of correction signalgenerator for linear equalizer.

FIG. 9 shows one embodiment of the FFT Implementation of the correctionsignal generator.

FIG. 10 shows a block diagram of one embodiment of blind mode adaptiveequalizer with hierarchical structure with decision feedback equalizer.

FIG. 11 shows one embodiment of the correction signal generator fordecision feedback equalizer.

FIG. 12 shows a block diagram of one embodiment of blind mode adaptiveequalizer with hierarchical structure and with orthogonalizer.

FIG. 13 shows one embodiment of correction signal vector normalizer.

FIG. 14 shows a block diagram of one embodiment of the cascadedequalizer.

FIG. 15 shows a block diagram of one embodiment of block diagram of theadaptive digital beam former system

FIG. 16 shows one embodiment of an example computer device.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The following description is provided to enable any person skilled inthe art to make and use the invention and sets forth the best modescontemplated by the inventor of carrying out his invention. Variousmodifications, however, will remain readily apparent to those skilled inthe art, since the generic principles of the present invention have beendefined herein specifically to provide systems and methods for blindmode equalization of signals received over time varying dispersivechannels, and for recovering the data symbols transmitted from a sourcein blind mode with adaptive beamformers.

FIG. 1 shows a block diagram for one of the various embodiments of theinvention. Referring to FIG. 1, the transmitted data symbol a_(k+ K) ₁ ,k+ K ₁=0, 1, . . . is in general a complex valued sequence of datasymbols taking values from a set of M possible values with K ₁ denotingsome reference positive integer. For example, for the case of the QPSKmodulation in digital communication systems, a_(k)=a_(I,k)+j a_(Q,k),with j=√{square root over (−1)}, and with a_(I,k) and a_(Q,k) denotingthe real and imaginary components of a_(k) taking possible values +A₀and −A₀ for some constant A₀>0. For the case of MQAM modulation with thenumber of points M in the signal constellation equal to N² for somepositive integer N that is normally selected to be an integer power of2, each of a_(I,k) and a_(Q,k) may take possible values from the set ofN values given by {±1, ±3, . . . , ±(N−1)}A₀. Similarly for the MPSKmodulation, a_(k) takes possible values from the set of M values givenby {A₀exp(j((2m−1)π/M); m=1, 2, . . . , M}. Referring to FIG. 1, thesequence of data symbols 1 a_(k+ K) ₁ is input to the discrete-timechannel where the impulse response h ^(cT) of the discrete-time channel2 is represented by a vector of length M=2M₁+1 given byh ^(cT) =[h _(−M) ₁ ^(c) . . . h ⁻¹ ^(c) h ₀ ^(c) h ₁ ^(c) . . . h _(M)₁ ^(c)]  (1)In (1) T denotes matrix transpose. The output of the discrete-timechannel is given by the convolution of the input data symbol sequencea_(k) with the channel impulse response h ^(cT) given in (2a). Theoutput 3 of the discrete-time channel is modified in the adder 5 by thechannel noise 4 n_(k+ K) ₁ ^(c) of variance 2σ_(n) ² generating thesignal z_(k+ K) ₁ ^(c). The noisy channel output signal 6 z_(k+ K) ₁^(c), given by (2b) is input to the blind mode adaptive equalizer system80.

$\begin{matrix}{{{y_{k_{0}} = {{\sum\limits_{i = {- M_{1}}}^{M_{1}}{h_{i}^{c*}a_{k_{0} - i}}} = {{\overset{\_}{h}}^{cH}\overset{\_}{x}}}};}{{\overset{\_}{x}}_{k_{0}} = \lbrack {a_{k_{0} + M_{1}},\ldots\mspace{14mu},a_{k_{0}},\ldots\mspace{14mu},a_{k_{0} - M_{1}}} \rbrack^{T}}} & ( {2a} ) \\{{{z_{k_{0}} = {y_{k_{0}} + n_{k_{0}}^{c}}};}{{k_{0} = {k + {\overset{\_}{K}}_{1}}};}{{k_{0} = 0},1,\ldots}} & ( {2b} )\end{matrix}$

In (2a), H denotes the matrix conjugate transpose operation and *denotes the complex conjugate operation.

Referring to FIG. 1, the noisy channel output signal 6 z_(k+ K) ₁ ^(c)is input to the channel gain normalizer block 7. The channel gainnormalizer estimates the average signal power at the output of thediscrete-time channel and normalizes the noisy channel output signal 6such that the signal power at the output of the channel gain normalize 7remains equal to some desired value even in the presence of thetime-varying impulse response of the discrete-time channel as is thecase with the fading dispersive channels in digital communicationsystems. The output 8 of the channel gain normalize 7 is given by

$\begin{matrix}{{{z_{k + K_{1}} = {{\sum\limits_{i = {- M_{1}}}^{M_{1}}{h_{i}^{*}a_{k + K_{1} - i}}} + n_{k + K_{1}}}};{{k + K_{1}} = 0}},1,2,\ldots} & (3)\end{matrix}$In (3) K₁= K ₁−N_(p) with N_(p) denoting the delay incurred in channelgain normalizer block 7 and {h_(i), i=M₁, . . . 0, . . . M₁} denotes thenormalized channel impulse response. Equation (3) may alternatively bewritten in the form of (4).z _(k) ₀ = h ^(H) x _(k) ₀ +n _(k) ₀ ; h ^(H) =[h _(−M) ₁ . . . h ⁻¹ h ₀h ₁ . . . h _(M) ₁ ]*;k ₀ =k+K ₁  (4)In (4) x _(k) ₀ is the channel state vector given by (2a).

Referring to FIG. 1, the output 8 of the channel gain normalize block 7z_(k+ K) ₁ is input to the level 1 adaptive system 40, of the blind modeadaptive equalizer with hierarchical structure (BMAEHS) 60, thatprovides the detected data symbols 12 a_(k+M) ₁ ^(d) at time k=−M₁,−M₁+1, . . . with N₁=K₁−M₁ denoting the equalizer delay. The level 1adaptive system 40 is comprised of an equalizer filter 9 with a timevarying equalizer parameter vector ŵ _(k) of length N=N₁+N₂+1 for somepositive integers N₁ and N₂ where N₁ and N₂ may be selected to be equal,an adaptation block 16 that adjusts the equalizer parameter vector 15 ŵ_(k), and the decision device 11 that detects the data symbol from theinput signal 10 present at the input of the decision device 11 based onthe decision function Δ( ). In various embodiments of the invention, theequalizer filter 9 may be a linear or a decision feedback filter, or amore general nonlinear equalizer filter characterized by a time varyingparameter vector 15 ŵ _(k). In one of the various embodiments of theinvention with the decision feedback equalizer, the detected symbol 12a_(k+M) ₁ ^(d) is fed back to the equalizer filter 9 via the delay block13 that introduces a delay of one sample as shown in FIG. 1. The output12 b of the delay 13 is inputted to the equalizer filter 9. In one ofthe various embodiments of the invention with the linear equalizer, theequalizer state vector 14 ψ _(k) is comprised of the equalizer inputz_(k+K) ₁ and the various delayed versions of z_(k+K) ₁ and is given byψ _(k) =[z _(k+K) ₁ , . . . ,z _(k+M) ₁ , . . . ,z _(k+M) ₁ _(−N) ₂]^(T) ;N ₂ =N ₁  (5)

In an alternative embodiment of the invention with the case of thedecision feedback equalizer filter, the equalizer state vector 14 ψ _(k)is also comprised of the various delayed versions of detected symbol 12a_(k+M) ₁ ^(d). Referring to FIG. 1, the gain normalizer output alsoreferred to as the normalized channel output 8 z_(k+K) ₁ , is input tothe delay 31 that introduces a delay of K₁ samples in the input 38 andprovides the delayed version 32 z_(k) to the model error estimator andthe correction signal generator (MEECGS) block 17 of the level 2adaptive system 50. Referring to FIG. 1, the detected data symbol 12 atthe output of the decision device 11, and the equalizer parameter vector15 ŵ _(k) are input to (MEECGS) block 17. The MEECGS block 17 estimatesthe channel impulse response vector h ^(T) from the detected symbol 12a_(k+M) ₁ ^(d) and the delayed normalized channel output 32 z_(k),determines any modeling error made by the level 1 adaptive system 40 andgenerates the correction signal 18 ŵ _(k) ^(c) ² to mitigate such amodeling error.

In the process of the blind mode equalization by the BMAEHS, theestimate of the data symbols 12 a_(k+M) ₁ during the initial period ofconvergence of the BMAEHS of length N_(d) has relatively highprobability of error. The initial period of convergence N_(d) is thetime taken by the BMAEHS 60 to achieve some relatively small meansquared equalizer error measured after the first N₁+1 samples at theoutput 8 of the channel gain normalize 7 are inputted to the BMAEHS 60and may be selected to be about 100-200 samples. The data symbols duringthe initial convergence period are recovered by the initial datarecovery block 75 of FIG. 1.

Referring to FIG. 1, the output 8 of the channel gain normalize 7z_(k+K) ₁ is inputted to the quantizer block 19. The quantizer 19 mayquantize the input samples to (n_(q)+1) bits with n_(q) denoting thenumber of magnitude bits at the quantizer output, so as to minimize thememory requirements for storing the initial segment of the channel gainnormalizer output. The number of quantizer bits may be selected on thebasis of the signal to noise power ratio expected at the noisy channeloutput signal 6 so that the variance of the quantization noise isrelatively small compared to the variance of the channel noise. Thesignal to quantization noise power ratio is given approximately by6(n_(q)+1) dB and a value of n_(q) equal to 3 may be adequate. Invarious other embodiments of the invention, the quantizer may beeliminated and the channel gain normalizer output 8 z_(k+K) ₁ may bedirectly inputted to the delay 21.

Referring to FIG. 1, the output of the quantizer 20 z_(k+K) ₁ ^(q) isinputted to the delay 21 that introduces a delay of N_(d) samples. Theoutput of the delay 21 is inputted to the fixed equalizer 24. The fixedequalizer is comprised of the cascade of the equalizer filter and thedecision device blocks similar to the equalizer filter 9 and thedecision device 11 blocks respectively of the BMAEHS 60. As shown inFIG. 1, initially the switch S₁ is in open position and the fixedequalizer parameter vector 33 ŵ _(k) ^(f) remains fixed at δ _(N) ₁_(,N) ₁ =[0 . . . 010 . . . 0] until the switch S₁ is closed. Atk+K₁=N_(I)≡N_(d)+N₁, the switch S₁ is closed and the fixed equalizerparameter vector 33 ŵ _(k) ^(f) is set equal to the equalizer parametervector 15 ŵ _(k) at the time of closing the switch and remains fixed fork+K₁>N_(I). The output of the fixed equalizer 25 a_(k+M) ₁ _(N) _(d)^(I),

M₁=K₁−N₁, is connected to the position 2 of the switch S₂ 26. Referringto FIG. 1, the detected symbol 12 a_(k+M) ₁ ^(d) is input to the delay29 that introduces a delay of N_(d) samples. The output 27 of the delay29 equal to a_(k+M) ₁ _(−N) _(d) ^(d) is connected to the position 3 ofthe switch S₂ 26. The position 1 of the switch S₂ 26 is connected to theground. For k+K₁<N_(I), the switch S₂ 26 remains in position 1 and theoutput of the switch S₂ 26 is equal to 0 during this period. During theperiod N_(I)≦k+K₁<N_(I)+N_(d), the switch S₂ 26 is connected to position2 and the final detected data 30 a_(k+M) ₁ _(−N) _(d) ^(d) ^(f) is takenfrom the output of the fixed equalizer 24. During the periodk+K₁≧N_(I)+N_(d), the output of the switch S₂ 26 is taken from theoutput of the BMAEHS 60. The output of the switch S₂ 26 constitutes thefinal detected data symbol 30 a_(k+M) ₁ _(−N) _(d) ^(d) ^(f) . Invarious other embodiments of the invention, the recovery of the initialdata segment may not be required and the initial data segment recoveryblock of FIG. 1 may not be present. In such alternative embodiments thefinal detected symbol output is taken directly from the output of theBMAEHS. As shown in FIG. 1, the detected symbol 12 a_(k+M) ₁ ^(d) may beinputted to the channel gain normalizer block 7.

FIG. 2 shows the block diagram of a digital communication system 101embodying the blind mode adaptive equalizer system 80 of FIG. 1.Referring to FIG. 2, the information data sequence 110 d_(i) possiblytaking binary values 0 and 1 is input to the error correction codeencoder and the interleaver block 111. The error correction coding andthe interleaving operations on the information data are performed toprotect the information data 110 d_(i) from the possible errors causeddue to various channel noise, disturbances, and interference. The codeddata bits sequence c_(i) at the output 112 of the error correction codeencoder and the interleaver block 111 may also be taking binary values.The coded data 112 c_(i) is input to the complex baseband modulator 113that groups a number m of coded data bits and maps the group into 1 outof M=2^(m) possible complex values representing points in the signalconstellation generating the sequence of the complex valued basebandsymbols b_(k) at the output 114 of the complex baseband modulator 113.For example, for the case of QPSK modulation corresponding to M=4,b_(k)=b_(I,k)+jb_(Q,k); j=√{square root over (−1)}, with b_(I,k) andb_(Q,k) each taking possible values A₀ and −A₀ for some positiveconstant A₀.

Referring to FIG. 2, the sequence of baseband symbols 114 b_(k) is inputto the differential encoder block 115. The differential encoder block115 transforms the sequence of baseband symbols 114 b_(k) into anothercomplex valued sequence of data symbols 116 a_(k) wherein the signalconstellation of a_(k) is same as that of the sequence b_(k). Forexample, for the case of the QPSK modulation witha_(k)=a_(I,k)+ja_(Q,k), both a_(I,k) and a_(Q,k) may take possiblevalues A₀ and −A₀. The differential encoder 115 protects the informationdata 110 against possible phase ambiguity introduced at the receiver.The phase ambiguity may arise, for example, in the generation of thereference carrier signal, not shown, using nonlinear processing of thereceived signal as by the use of a fourth power nonlinearity in the caseof QPSK modulation. The phase ambiguity may also occur in the use of theblind mode adaptive equalizer and may have a value of 2πn/M with n=0, 1,. . . , (M−1) for the case of MPSK modulation with M=4 for the QPSKmodulation. More generally the number of phase ambiguities arising dueto the blind mode equalizer may be equal to the number of distinct phaserotations of the signal constellation diagram that leaves the signalconstellation diagram invariant.

Referring to FIG. 2 the sequence of the data symbols 116 a_(k) at theoutput of the differential encoder 115 is inputted to the band limitingfilter 117. The band limiting filter 117 may be a square root raisedcosine filter used to minimize the bandwidth required for thetransmission of the modulated RF signal. With the use of the square rootraised cosine filter the absolute bandwidth of the filtered signal u_(k)at the output 118 of the band limiting filter is reduced to R_(s)(1+r)/2where R_(s) is the symbol rate of the data symbols a_(k) and r with0<r≦1 denotes the filter roll off factor as compared to a zero crossingbandwidth of the input data symbol sequence a_(k) equal to R_(s). Theband limited symbol sequence 118 u_(k) is inputted to the complexbaseband to RF converter block 119 that shifts the center frequency ofthe spectrum of the signal 118 u_(k) to the RF or possibly anintermediate (IF) frequency. The complex baseband to RF converter block119 may in general have several stages including the conversion to theRF or some intermediate frequency (IF), and digital to analogconversion. The RF signal 120 u_(RF)(t) at the output of the complexbaseband to RF converter block 119 is inputted to the RF back end block121 that is comprised of the RF band pass filter, the power amplifier,and possibly conversion from IF to RF frequency. The amplified signal122 u_(T)(t) is connected to the transmit antenna 123 for transmissionof the RF signal into the wireless channel that may exhibit multipathpropagation and fading resulting in the introduction of the inter symbolinterference (ISI) in the transmitted signal.

Referring to FIG. 2 the RF signal at the output of the wireless channelis received by the receive antenna 124 providing the received RF signal125 v_(R)(t) to the input of the RF front end block 126 of receiver 100.The RF front end block may be comprised of a low noise amplifier (LNA),RF band pass filter, other amplifier stages, and possibly conversionfrom RF to IF and provides the amplified RF signal 127 v_(RF)(t) at theoutput of the RF front end block. The receive antenna 124 and the RFfront end block 126 may introduce additive noise including the thermalnoise into the signal RF signal in the process of receiving andamplifying the RF signal at the output of the wireless channel.Referring to FIG. 2, the amplified RF signal 127 is inputted to the RFto complex baseband converter block 128 that down converts the RF signalto the complex baseband signal 129. The RF to complex baseband converterblock 128 may be comprised of a RF to IF down converter, the IF tocomplex baseband converter and an analog to digital converter. Thecomplex baseband signal 129 v_(k) at the output of the RF to complexbaseband converter block 128 is inputted to band limiting matched filterblock 130 that may be comprised of a band limiting filter that ismatched to the band limiting filter used at the transmitter and a downsampler. For the case of square root raised cosine filter used as theband limiting filter 117 at the transmitter, the band limiting filter130 at the receiver is also the same square root raised cosine filter117 at the transmitter. The design of the band limiting matched filterblock 130 and various other preceding blocks both in the transmitter andreceiver are well known to those skilled in the art of the field of thisinvention.

Referring to FIG. 2 the output 6 z_(k+ K) ₁ ^(c), with K ₁ denoting somereference positive integer, of the band limiting matched filter block130 is inputted to the blind mode adaptive equalizer system 80. Theblind mode adaptive equalizer system is comprised of the channel gainnormalizer 7, the blind mode adaptive equalizer with hierarchicalstructure (BMAEHS) 60 and the initial data segment recovery circuit 75.The details of the blind mode adaptive equalizer system 80 are shown inFIG. 1. The cascade of the various blocks comprised of the band limitingfilter 117, complex baseband to RF converter 119, the RF back end 121and the transmit antenna 123, at the transmitter, wireless communicationchannel, and the receive antenna 124, the RF front end 126, RF tocomplex baseband converter 128 and the band limiting matched filter 130at the receiver may be modeled by the cascade comprised of an equivalentdiscrete time channel 2 with input symbols a_(k+ K) ₁ with K ₁ denotingsome positive reference integer wherein a channel noise 4 n_(k+ K) ₁ isadded to the output of the channel 2 as shown in FIG. 1. The equivalentdiscrete time channel may have some unknown impulse response h ^(c) thatmodels the combined response of all the blocks in the said cascade.

Referring to FIG. 2, the channel gain normalizer 7 estimates the averagesignal power at the output of the equivalent discrete-time channel andnormalizes the noisy channel output such that the signal power at theoutput of the channel gain normalizer remains equal to some desiredvalue even in the presence of the time-varying impulse response of thediscrete-time channel as is the case with the fading dispersive channelsin the digital communication system of the FIG. 2. The BMAEHS 60mitigates the impact of the inter symbol interference that may be causedby the multipath propagation in the wireless channel without requiringany knowledge of the channel impulse response or the need of anytraining sequence. The detected symbols during the initial convergencetime of the BMAEHS may have relatively large distortion. The initialdata segment recovery block 70 of FIG. 2 reconstructs the detectedsymbols during the initial convergence time based on the convergedparameters of the BMAEHS and pre appends to the detected symbols at theoutput of the BMAEHS after the initial convergence time therebymitigating the ISI from the initial data segment as well. The sequenceof the final detected data symbols 30 a_(k+M) ₁ _(−N) _(d) ^(d) ^(f)with N_(d) denoting the initial convergence time for the BMAEHS and M₁ apositive integer, the output of the blind mode adaptive equalizer systemare inputted to the differential decoder block 131. The differentialdecoder block 131 performs an inverse operation to that performed in thedifferential encoder block 115 at the transmitter generating thesequence of the detected baseband symbols 132 b_(k+M) ₁ _(−N) _(d) atthe output.

FIG. 3A shows the block diagram of the differential encoder 115 unit ofFIG. 2 for the modulated signal such as QAM, MPSK or ASK. As shown inFIG. 3A, the baseband symbol b_(k) is inputted to the tan₂ ⁻¹( ) block203 that provides the four quadrant phase θ_(b,k) of the input b_(k) atthe output with taking values between 0 and 2π. The phase θ_(b,k) isinputted to the phase threshold device 205 that provides the output 206θ_(r,k) according to the decision function D_(p)( ) given by equation(6).θ_(r,k) =D _(p)(θ_(b,k))=φ_(i);φ_(t) _(i) ≦θ_(b,k)<φ_(t) _(i+1) ;i=0,1,. . . ,S−1  (6)

In (6) S denotes the order of rotational symmetry of the signalconstellation diagram of the baseband signal b_(k) equal to the numberof distinct phase rotations of the signal constellation diagram thatleave the signal constellation unchanged and is equal to the number ofphase ambiguities that may be introduced by the blind mode equalizer. In(6) φ_(t) _(i) ; i=0, 1, . . . , S−1 are the S threshold levels of thephase threshold device 205.

For illustration, FIG. 3B shows the signal constellation diagram of the16 QAM signal that has order of rotational symmetry S equal to 4 withthe possible phase ambiguities equal to 0, π/2, π, 3π/2 as the rotationof the signal constellation diagram by any of the four values 0, π/2, π,3π/2 leaves the signal constellation unchanged. The threshold levels forthe 16 QAM signal are given by. φ_(t) ₀ =0, =π/2, φ_(t) ₂ =π, φ_(t) ₃=3π/2. The range of the phase given by φ_(t) _(i) ≦θ_(b,k)<φ_(t) _(i+1)defines the i^(th) sector of the signal constellation diagram equal tothe i^(th) quadrant of the signal constellation diagram in FIG. 3B fori=0, 1, 2, 3. Referring to FIG. 3A the output of the phase thresholddevice 205 is equal to the reference phase φ_(i) for the i^(th) sectorif θ_(b) lies in the i^(th) sector or quadrant. The output of the phasethreshold device 205 base phase 206 θ_(r,k) is equal to one of the Spossible values Referring to FIG. 3A, the minimum reference phase φ₀ issubtracted from the base phase 206 θ_(r,k) by the adder 209. The output215 θ_(a) of the adder 209 is inputted to the phase accumulator 210comprised of the adder 216, mod 2π block 218 and delay 222, provides theoutput 221 θ_(c,k) according to equation (2b).

$\begin{matrix}{{{\theta_{c,k} = {\underset{2\pi}{mod}( {\theta_{i,k} + \theta_{c,{k - 1}}} )}};}{{k = 0},1,{\ldots\mspace{14mu};}}{\theta_{c,{- 1}} = 0}} & (7)\end{matrix}$In (7) the mod 2π operation is defined as

$\begin{matrix}{{\underset{2\pi}{mod}(x)} = {x - {\lfloor \frac{x}{2\pi} \rfloor 2\pi}}} & (8)\end{matrix}$

In (8) └x┘ denotes the highest integer that is smaller than x for anyreal x. The use of mod 2π block 218 in FIG. 3A is to avoid possiblenumerical build up of the accumulator output phase 221 by keeping theaccumulator output 221 within the range 0 to 2π for all values of timek.

Referring to FIG. 3A, the phase accumulator output 221 is inputted tothe adder 224 that adds the phase φ₀ providing the output 226 θ_(p,k) tothe adder 227. Referring to FIG. 3B for the case of 16QAM constellation,φ₀=π/4 and φ_(i,k) takes possible values 0, π/2, π, 3π/2. The output 221θ_(c,k) of the phase accumulator can also have 0, π/2, π, 3π/2 as theonly possible values. The output 226 θ_(p,k) of the differential phaseencoder 220 has π/4, 3π/4, 5π/4, 7π/4 as the only possible values.

Referring to FIG. 3A, the signal 206 θ_(r,k) is subtracted from thesignal 204 θ_(b,k) by the adder 207 providing the output 208 θ_(d,k) tothe adder 227 that adds 208 θ_(d,k) to the differential phase encoderoutput 226 θ_(p,k) providing the phase of the encoded signal 228 θ_(a,k)at the output. The phase 228 θ_(a,k) is inputted to the block 231providing the output 231 exp[jθ_(a,k)]; j=√{square root over (−1)} tothe multiplier 232. Referring to FIG. 3A, the baseband symbol b_(k) isinputted to the absolute value block 201 that provides the absolutevalue 202 |b_(k)| to the multiplier 232. The output 116a_(k)=|b_(k)|exp(jθ_(a,k)); j=√{square root over (−1)} of the multiplier232 is the differentially encoded data symbol a_(k). The process ofdifferential encoding leaves the magnitude of the symbol unchanged with|a_(k)|=|b_(k)| and with only the symbol phase modified.

As an example of the differential encoding process, FIG. 3B illustratesthe encoding for the 16QAM signal. In FIG. 3B, the subscript k onvarious symbols has been dropped for clarity. Referring to FIG. 3B, thesignal point b_(k)=(A₀+j2A₀); j=√{square root over (−1)}, marked by thesymbol

in FIG. 3B, is encoded into the signal point a_(k)=(A₀−j2A₀); j=√{squareroot over (−1)} marked by the symbol

in the figure. Referring to FIG. 3B, the phase θ_(r) is equal to φ₀=π/4,with the corresponding phase 215 θ_(i) equal to 0. In the illustrationof FIG. 3B, φ_(c,k−1) is equal to π resulting in phase θ_(c,k) equal toπ. Addition of φ₀=π/4 to θ_(c,k) results in the phase 226 θ_(p) equal to5π/4 that is equal to φ₂. Addition of phase 208 θ_(d) equal to tan₂⁻¹(3/1)−π/4≅0.15π to the phase θ_(p)=5π/4 results in θ_(a)=1.4π as shownin FIG. 3B. With the magnitude of a_(k) given by |a_(k)|=A₀√{square rootover (10)}, the encoded data symbol a_(k)=A₀√{square root over(10)}exp(j1.4π); j=√{square root over (−1)} is obtained as shown in FIG.3B by the symbol

. For the case of the PSK signals, the phase threshold device 205 D_(p)() is bypassed with the output 206 θ_(r,k) equal to the phase 204 θ_(b,k)and with the phase 208 θ_(d,k) equal to 0.

FIG. 4 shows the block diagram of the differential decoder 131 unit ofFIG. 2. Referring to FIG. 4 the detected data symbol a_(k) ^(d), isinputted to the tan₂ ⁻¹( ) block 242 providing the phase θ_(a,k) ofa_(k) ^(d) at the output 243. The phase 243 θ_(a,k) is inputted to thephase threshold device 245 that provides the output phase 244 θ_(o,k)computed according to the decision function D_(p)( ) given by equation(6). The output of the phase threshold device 245 is inputted to thedifferential phase decoder 270 providing the phase θ_(r,k) at the output259. Referring to FIG. 4, the phase 244 θ_(o,k) is inputted to the adder246 that subtracts φ₀ from θ_(r,k) with the output 250θ_(q,k)=θ_(o,k)−φ₀. The phase θ_(q,k) is inputted to the delay 251providing the delayed phase 252 θ_(q,k−1) to the adder 254 thatsubtracts θ_(q,k−1) from θ_(q,k) providing the output 255θ_(i,k)=θ_(q,k)−θ_(q,k−1) to the adder 258 that adds φ₀ to the input 255φ_(i,k) providing the output 259 θ_(r,k) to the adder 260. Referring toFIG. 4, the phase 243 θ_(a,k) and 244 θ_(o,k) are inputted to the adder246 providing the phase difference 247 θ_(d,k)=φ_(a,k)−θ_(o,k) to theinput of the adder 260 that adds θ_(d,k) to the phase 259 θ_(r,k)providing the phase 261 θ_(b,k) that is the phase of the differentiallydecoded signal b_(k) ^(d).

Referring to FIG. 4, the detected data symbol 30 a_(k) ^(d) is inputtedto the absolute value block 240 providing the absolute value 241 |a_(k)^(d)| to the multiplier 262. The output 261 θ_(b,k) is inputted to theblock 264 providing the output 263 exp[jθ_(b,k)]; j=√{square root over(−1)} to the multiplier 262. The multiplier 262 provides the datadetected symbol 132 b_(k) ^(d)=|a_(k) ^(d)|exp(jθ_(b,k)); j=√{squareroot over (−1)} at the multiplier 262 output.

Referring to FIG. 2, the detected baseband symbols 132 are input to thecomplex baseband to data bit mapper 133 that maps the complex basebandsymbols 132 into groups of m binary bits each based on the mapping usedin the complex baseband modulator block 113 at the transmitter. Thesequence of the detected coded data bits 134 ĉ_(i) at the output of thecomplex baseband to data bit mapper block 133 is inputted to the errorcorrection code decoder and deinterleaver block 135 that performsinverse operations to those performed in the error correction codeencoder and interleaver block 111 at the transmitter and provides thedetected information data sequence 136 {circumflex over (d)}_(i) at theoutput. In some communication systems, the band limiting filter mayintentionally introduce some ISI caused by selecting the symbol rate tobe higher than the Nyquist rate so as to increase the channel capacity.The blind mode adaptive equalizer system 80 of FIG. 1, 2 will alsomitigate the ISI arising both due to the intentionally introduced ISIand that arising from the wireless channel.

FIG. 5 shows the block diagram of the channel gain normalizer 7.Referring to FIG. 5, the noisy channel output 6 z_(k) ₀ ^(c), k₀=k+ K ₁,with K ₁ equal to a reference positive integer, is input to the channelpower estimator block 370 that estimates the average power present atthe noisy channel output 6. The noisy channel output 6 is input to thenorm square block 310 that provides ζ_(k) ₀ =|z_(k) ₀ ^(c)|² at theoutput 311. The output of the norm square block 310 is inputted to theaccumulator 1 320 that accumulates the input 311 ζ_(k) ₀ over a periodof time with an exponential data weighting providing the accumulatedvalue 313 ζ_(k) ₀ ^(a) at the output withζ_(k) ₀ ^(a)=λ_(p)ζ_(k) ₀ ⁻¹ ^(a)+ζ_(k) ₀ ;k ₀=0,1, . . .   (9)In (9) the initial value of the accumulator output ζ⁻¹ ^(a) is set equalto 0, and λ_(P), 0<λ_(p)≦1, is a constant that determines the effectiveperiod of accumulation in the limit as k₀→∞ and is approximately equalto 1/(1−λ_(p)), for example, λ_(P) may be selected equal to 0.998.Referring to FIG. 1, a constant 1 is input to the accumulator 2 block330 that provides at its output 330 κ_(k) ₀ ^(p) given byκ_(k) ₀ ^(p)=λ_(p)κ_(k) ₀ ⁻¹ ^(p)+1;κ⁻¹ ^(p)=0;k ₀=0,1, . . .   (10)

From (10), the value of κ_(k) ₀ ^(p) is given by κ_(k) ₀ ^(p)=(1−λλ_(p)^(k) ⁰ ⁺¹)/(1−λ_(p)); k₀=0, 1, . . . . The outputs of the accumulators 1and 2 blocks 320 and 330 are inputted to divider 341 that divides theoutput 313 ζ_(k) ₀ ^(a) of the accumulator 320 by the output 333 κ_(k) ₀^(p) of the accumulator 330 providing the average power estimate 342P_(T,k) ₀ =ζ_(k) ₀ ^(a)/κ_(k) ₀ ^(p) at the output of the divider 341.

Referring to FIG. 5, the average power estimate 342 P_(T,k) ₀ is inputto the adder 343 that subtracts the estimate of the noise variance 3442{circumflex over (σ)}_(n) ² from 342 P_(T,k) ₀ resulting in theestimate 345 P_(c,k) ₀ of the signal power at the discrete-time channel2 output. The noise variance estimate 344 may be some a-priori estimateof the channel noise variance or may be set equal to 0. The signal powerestimate 345 P_(c,k) ₀ is input to the divider 349 that has its otherinput made equal to the desired signal power 346 P_(s)=E[|a_(k)|²] withE denoting the expected value operator. The desired signal power may benormalized by an arbitrary positive constant, for example by A₀ ² withA₀ simultaneously normalizing the threshold levels in (23)-(24) of thedecision device 11 and the expected value E[|a_(k)|_(c)] in (14), (15).The divider 349 block divides the signal power estimate 345 P_(c,k) ₀ by346 P_(s) and outputs the result 350 P_(G,k) ₀ =P_(c,k) ₀ /P_(s). Thedivider 349 output 350 P_(G,k) ₀ representing the discrete-time channelpower gain is input to the square root block 351 that provides thechannel gain 352 G_(k) ₀ =√{square root over (P_(G,k) ₀ )} at the outputof the square root block. The channel gain G_(k) ₀ is made available tothe multiplier 353. The initial convergence rate of the BMAEHS 60 may beincreased by adjusting the channel gain G_(k) by a factor α_(k) that isderived on the basis of the statistics of the detected symbol a_(k) ^(d)at the output 12 of the BMAEHS. The adjustment factor α_(k) is derivedsuch that the expected value of the magnitude of the real and imaginarycomponents of a_(k) ^(d)=a_(I,k) ^(d)+ja_(Q,k) ^(d); j=√{square rootover (−1)} approach E[|a_(I,k)|] and [|a_(Q,k)|];a_(k)=a_(I,k)+ja_(Q,k), respectively with convergence, where E denotesthe expected value operation. Referring to FIG. 5, the detected symbola_(k+M) ₁ is inputted to the absolute value ∥_(c) block 372. where inthe operation of the absolute value block 372 for any complex valuedargument z is defined by|z| _(c) =|z _(r) |+j|z _(i) |;z=z _(r) +jz _(i) ;j=√{square root over(−1)};z _(r) ,z _(i)real  (11)

Referring to FIG. 5, the output 373

a_(k + M₁)^(d)_(c)of the absolute value block 372 is inputted to the switch S 374 that isclosed at k+M₁=N_(p)+N₁+1 and remains closed thereon where N₁ is thedelay introduced by the BMAEHS block 60. The output 374 ν_(k) 374 of theswitch S is inputted to the averaging block 395 that averages the inputν_(k) over consecutive periods of n_(s) samples. The averaging periodn_(s) may be selected to be equal to 10. The averaging block iscomprised of the delay 376, adder 377, delay 379, down sampler 385, andmultiplier 382. Referring to FIG. 5, the output of switch S is inputtedto the adder 377 and to the delay 376 that provides the delayed versionν_(k−n) _(s) to the adder 377. The output of the adder 377 ν_(k) ^(s) isinput to the delay 379 providing output 380 ν_(k−1) ^(s) to the input ofthe adder 377. The output of the adder 377 may be written as

$\begin{matrix}{{{v_{k}^{s} = {v_{k - 1}^{s} + v_{k} - v_{k - n_{s}}}};}{{v_{0}^{s} = 0};}{v_{k}^{s} = {\sum\limits_{j = {k - n_{s} + 1}}^{k}v_{j}}}} & (12)\end{matrix}$The output ν_(k) ^(s) of the adder 377 is inputted to the down sampler385 that samples the input 378 at intervals of n_(s) samples with theoutput 381 ν_(|) ^(s) inputted to the multiplier 382. The multiplier 382normalizes the input ν_(I) ^(s) by n_(s) providing the average outputν_(|) ^(a) given by

$\begin{matrix}{{{{{v_{❘}^{a} = {\frac{1}{n_{s}}{\sum\limits_{i = {{{({❘{- 1}})}n_{s}} + 1}}^{❘n_{s}}v_{i}}}};}❘} = 1},2,\ldots} & (13)\end{matrix}$The output ν_(|) ^(a) of the averaging block 395 is inputted to thedivider block 386 that divides ν_(|) ^(a) by input 384 E[|a_(k)|_(c)]given byE[|a _(k)|_(c) ]=E[|a _(I,k) |]+jE[|a _(Q,k) |];a _(k) =a _(I,k) +ja_(Q,k) ;j=√{square root over (−1)}  (14)

For example, when both a_(I,k) and a_(Q,k) take possible values ±A₀ and±3A₀ with equiprobable distribution, thenE[|a _(k)|_(c)]=2A ₀ +j2A ₀ ;j=√{square root over (−1)}  (15)

Referring to FIG. 5, the output of the divider 386 e_(|) ^(m)=ν_(|)^(a){E[|a_(k)|_(c)]}⁻¹ may measure the deviation of the magnitude of thereal and imaginary components of the BMAEHS 60 output from the expectedvalues E[|a_(I,k)|] and E[|a_(Q,k)|] respectively. The magnitude errore_(|) ^(m) is inputted to the multiplier 388 that multiplies e_(|) ^(m)by a relatively small positive number μ_(a) providing the output 389equal to μ_(a)e_(|) ^(m) the input of the adder 392. The output of theadder α_(l) is inputted to the delay 391. The output 394 α_(l−1) of thedelay 391 is inputted to the adder 390 that provides the output 392α_(l) according toα_(|)=α_(|−1)+μ_(a) e _(|) ^(m);|=1,2, . . . ;α₀=1  (16)

The output 392 α_(l) of the adder 390 is inputted to the up samplerblock 393 that increases the sampling rate by a factor n_(s) usingsample hold. The output 396 α_(k) ₀ of the sampler block 393 is inputtedto the multiplier 353 that adjusts the channel gain estimate G_(k) ₀ byα_(k) ₀ providing the output 354 G_(k) ₀ ^(m) to the divider 365.

Referring to FIG. 5, the noisy channel output 6 z_(k) ₀ ^(c) is input todelay block 361 that introduces a delay of N_(p) samples that is thenumber of samples required to provide a good initial estimate of G_(k) ₀^(m) and may be selected equal to 50. The output of the delay block 361is input to the divider 365 that normalizes the delay block output 362by the modified channel gain 354 G_(k) ₀ ^(m) providing the normalizedchannel output 8 z_(k+K) ₁ ; k+K₁=0, 1, . . . , with K₁= K ₁−N_(p).

The parameter α_(k) matches the amplitude of the real and imaginarycomponents of the normalized channel output to the threshold levels ofthe slicers in the decision device, thereby also making the probabilitydistribution of the detected data symbols a_(k) ^(d) equal to theprobability distribution of the data symbols a_(k). This can also beachieved in an alternative embodiment of the invention by making thedominant center element h₀ of the normalized channel impulse response hequal to 1. For the case when both the data symbols and the channelimpulse response vector are real valued, the parameter α_(k) may beestimated in terms of the channel dispersion defined as

$\begin{matrix}{d = \{ {1 - \frac{{h_{0}}^{2}}{{\overset{\_}{h}}^{2}}} \}^{1/2}} & (17)\end{matrix}$Thus for the normalized channel with ∥ h∥=1, the estimate of themagnitude of α_(k) in terms of the channel dispersion d is given byα_(k)=√{square root over ((1−d ²))}  (18)

For the case of weakly dispersive channels wherein d is much smallercompared to 1, α_(k) may be estimated to be 1. For the case of datasymbols having constant amplitude as is the case, for example, with MPSKmodulation the parameter α_(k) may also be set to 1. In the more generalcase of the complex valued data symbols with non constant amplitude, inalternative embodiments of the invention, the parameter may be estimatedadaptively so as to make the dominant element of the normalized channelimpulse response approach 1. An algorithm that minimizes the differencebetween the dominant element h₀ and 1 is given by

$\begin{matrix}{{\alpha_{k + 1} = {\alpha_{k} +}}{{\mu_{a}\frac{{\hat{h}}_{0,k}}{\alpha_{k}}( {1 - {\alpha_{k}{\hat{h}}_{0,k}}} )^{*}};}{{k = 0},1,\ldots}} & (19)\end{matrix}$In equation (19) μ_(a) is some small positive constant and α₀ may be setto 1.

In various embodiments of the invention, the equalizer filter in theequalizer filter block may be a linear, a decision feedback or a moregeneral nonlinear equalizer filter based on the equalizer parametervector ŵ _(k) that provides the linear estimate of the data symbol onthe basis of the normalized channel output z_(k+K) ₁ .

FIG. 6 shows the block diagram of the BMAEHS 60 of FIG. 1 in one of thevarious embodiments of the invention. Referring to FIG. 6, the equalizerfilter 9 is a linear equalizer filter. Referring to FIG. 6, the outputof the channel gain normalizer block 8 also referred to as thenormalized channel output z_(k+K) ₁ is input to a cascade of 2N₁ delayelements 401 providing the delayed versions 402 of z_(k+K) ₁ denoted byz_(k+K) ₁ ⁻¹, . . . , z_(k−N) ₁ _(+M) ₁ at their respective outputs. Thenormalized channel output and its various delayed versions 402 are inputto the N wm multipliers 403 wm₁, . . . , wm_(N). The N wm multipliers403 are inputted by the conjugates 406 of the components 405 of theequalizer parameter vector ŵ_(−N) ₁ _(,k), . . . , ŵ_(0,k), . . . ,ŵ_(N) ₁ _(,k). The wm multipliers 403 wm₁, . . . , wm_(N) multiply thenormalized channel output and its delayed versions 402 by the respectiveconjugates 406 of the components of the equalizer parameter vector ŵ_(k) generating the respective products 407 at the outputs of the wmmultipliers 403. The outputs of the wm multipliers 407 are inputted tothe summer 408 providing a linear estimate 10 â_(k+M) ₁ of the datasymbol at the output of the summer 408. The linear estimate 10 â_(k+M) ₁is input to the decision device 11 that generates the detected symbol 12a_(k+M) ₁ ^(d) at the output of the decision device 11 based on thedecision function Δ( ).

The selection of the decision function Δ( ) depends upon the probabilitydistribution of the data symbols a_(k)=a_(I,k)+j a_(Q,k), withj=√{square root over (−1)}, and with a_(I,k) and a_(Q,k) denoting thereal and imaginary components of a_(k). For example, for the case of thediscrete type of the probability distribution of the data symbols a_(k)with both the real and imaginary components a_(I,k) and a_(Q,k) of a_(k)taking possible values from the finite sets Σ_(I) and Σ_(Q) respectivelyand where the components a_(I,k) and a_(Q,k) are statisticallyindependent as is the case, for example, for the MQAM modulated signals,the decision function may be given by (20).D(â _(I,k) +jâ _(Q,k))=D _(I)(â _(I,k))+jD _(Q)(â _(Q,k))  (20)In (20) the functions Δ_(I)( ) and Δ_(Q)( ) may be the slicer functions.For the specific case when both the sets Σ_(I) and Σ_(Q) are equal tothe set {±1, ±3, . . . , ±(N−1)} A₀ for some integer N and positive realnumber A₀, the two slicer functions Δ_(I)(x) and Δ_(Q)(x) with x real,are identical and are given by (21).D _(I)(x)=D _(I)(x)=D _(m)(|x|)sgn(x)  (21)In (21), sgn(x) is the signum function given by

$\begin{matrix}{{{sgn}(x)} = \{ \begin{matrix}{{+ 1};{x > 0}} \\{{- 1};{x \leq 0}}\end{matrix} } & (22)\end{matrix}$And the function D_(m) (|x|) is given byD _(m)(|x|)=iA ₀ ;V _(t) _(i−1) ≦|x|<V _(t) _(i) ;i=1,2, . . .,N/2  (23)In (23), V_(t) _(i) for i=0, 1, . . . , N/2 are the threshold levelsgiven by

$\begin{matrix}{V_{t_{i}} = \{ \begin{matrix}{0;{i = 0}} \\{{2{iA}_{0}};{0 < i < {N/2}}} \\{\infty;{i = {N/2}}}\end{matrix} } & (24)\end{matrix}$

The decision function described by (20) (24), for example, applies tothe case where a_(k) is obtained as a result of MQAM modulation in thedigital communication system of FIG. 2, with the number of points in thesignal constellation M=N². For other modulation schemes and differentprobability distributions of the data symbol, other appropriate decisionfunctions may be employed. For the specific case of M=4 corresponding tothe QPSK modulation, the decision function in (20) reduces toD(â _(I,k) +jâ _(Q,k))=sgn(â _(I,k))+jsgn(â _(Q,k))  (25)

For the case of MPSK modulation with M>4, the decision device maycomprise of a normalizer that normalizes the complex data symbol by itsmagnitude with the normalized data symbol operated by the decisionfunction in (20)-(24).

Referring to FIG. 6, the linear estimate 10 â_(k+M) ₁ is subtracted from12 a_(k+M) ₁ ^(d) by the adder 409 providing the error signal 410e_(k)=(a_(k+M) ₁ ^(d)−â_(k+M) ₁ ). The error signal 410 e_(k) is inputto the conjugate block 411. The output of the conjugate block 412 e_(k)*is multiplied by a positive scalar 413 μ_(d) in the multiplier 414. Theoutput of the multiplier 414 is input to the N weight correctionmultipliers 415 wcm₁, . . . , wcm_(N) wherein it multiplies thenormalized channel output z_(k+K) ₁ and its various delayed versions 401z_(k+K) ₁ ⁻¹, . . . , z_(k−N) ₁ _(+M) ₁ generating the N components 419of μ_(d) w _(k) ^(c) ¹ with the first correction vector w _(k) ^(c) ¹given by (26).w _(k) ^(c) ¹ = ψ _(k) e _(k)*; ψ _(k) =[z _(k+K) ₁ , . . . ,z _(k+M)_(M) ₁ , . . . ,z _(k+M) ₁ _(−N) ₁ ]^(T);  (26a)e _(k)=(a _(k+M) ₁ ^(d) −â _(k+M) ₁ );k=0,1, . . .   (26b)

Referring to FIG. 6, the second parameter correction vector 452 w _(k)generated by the MEECGS for LEQ block 50 is multiplied by a positivescalar 453 μ by the multiplier 454. The multiplier output 455 isconnected to the vector to scalar converter 460 that provides the Ncomponents 461 of the vector μ w _(k) ^(c) ² given by μw_(−N) ₁ ^(c) ² ,. . . , μw_(0,k) ^(c) ² , . . . , μw_(N) ₁ _(,k) ^(c) ² at the output ofthe vector to scalar converter 460. The outputs 419 of the wcm₁, . . . ,wcm_(N) multipliers 415 and the N components 461 of the vector μ w _(k)^(c) ² are both input to N adders 420 wca₁, . . . , wca_(N). Referringto FIG. 6, the equalizer parameter components, ŵ_(−N) ₁ _(,k), . . . ,ŵ_(0,k), . . . , ŵ_(N) ₁ _(,k) at the outputs of the N delay elements421 are input to the wca adders 420. The wca adders 420 add theequalizer parameter components 422 ŵ_(−N) ₁ _(,k), . . . , ŵ_(0,k), . .. , ŵ_(N) ₁ _(,k) to the outputs 419 of the wcm₁, . . . , wcm_(N)multipliers and subtract the N components 461 of the vector μ w _(k)^(c) ² from the results of the addition providing the updated version ofthe N components 422 of the equalizer parameter vector ŵ _(k±1) at theoutputs of the N wca adders 420. The output 422 of the N wca adders 420are connected to the N delay elements 421. The outputs 405 of the Ndelay elements 421 are equal to the equalizer parameter vectorcomponents 405 ŵ_(−N) ₁ _(,k), . . . , ŵ_(0,k), . . . , ŵ_(N) ₁ _(,k)that are inputted to the N conjugate blocks 404.

Referring to FIG. 6, the detected symbol 12 a_(k+M) ₁ ^(d) is inputtedto the channel estimator 440. The normalized channel output 8 z_(k+K) ₁is input to the delay block 435 that introduces a delay of K₁ samplesproviding the delayed version 436 z_(k) to the input of the channelestimator 440. The channel estimator 440 provides the estimate of thechannel impulse response vector 442 ĥ _(k) at the output of the channelestimator. The equalizer parameters 405, ŵ_(−N) ₁ _(,k), . . . ,ŵ_(0,k), . . . , ŵ_(N) ₁ _(,k) are input to the scalar to vectorconverter 430 that provides the equalizer vector 432 ŵ _(k) to thecorrection signal generator for LEQ 450. The estimate of the channelimpulse response vector 442 ĥ _(k) is input to the correction signalgenerator 450 that provides the second correction signal vector 452 w_(k) ^(c) ² to the multiplier 454. The correction signal generator 450convolves the estimate of the channel impulse response vector 442 ĥ _(k)^(T) with the equalizer parameter vector 432 ŵ _(k) to obtain theconvolved vector ĝ _(k) ^(T). The difference between the vector ĝ _(k)^(T) obtained by convolving the estimate of the channel impulse responsevector ĥ _(k) ^(T) with the equalizer parameter vector ŵ _(k) ^(T), andthe ideal impulse response vector

${\overset{\_}{\delta}}_{K_{1},K_{1}}^{T} = \begin{bmatrix}\underset{\underset{K_{1}}{︸}}{00\mspace{14mu}\ldots\mspace{14mu} 0} & 1 & \underset{\underset{K_{1}}{︸}}{00\mspace{14mu}\ldots\mspace{14mu} 0}\end{bmatrix}$may provide a measure of the modeling error incurred by the equalizer 9.A large deviation of the convolved response ĝ _(k) ^(T) from the idealimpulse response implies a relatively large modeling error. Thecorrection signal generator block generates a correction signal 452 w_(k) ^(c) ² on the basis of the modeling error vector [ δ _(K) ₁ _(,K) ₁− ĝ _(k)] and inputs the correction signal 452 w _(k) ^(c) ² to theadaptation block 16 for adjusting the equalizer parameter vector ŵ_(k+1) at time k+1.

The equalizer parameter update algorithm implemented in FIG. 6 may bedescribed by (27a, b)ŵ _(k+1) = ŵ _(k)+μ_(d) ŵ _(k) ^(c) ¹ −μ ŵ _(k) ^(c) ² ;  (27a)ŵ _(k) ^(c) ¹ = ψ _(k)(a _(k+M) ¹ ^(d) − ŵ _(k) ^(H) ψ _(k))*;k=0,1, . ..   (27b)The first correction signal vector w _(k) ^(c) ¹ may be based on theminimization of the stochastic function |a_(k+M) ₁ ^(d)− w ^(H) ψ _(k)|²with respect to the parameter vector w and is equal to 0.5 times thenegative of the gradient of the stochastic function with respect to w.In the absence of the second correction signal vector, the updatealgorithm in (27a) reduces to the decision directed version of the LMSalgorithm.

In various other embodiments of the invention, the first correctionsignal vector may be derived on the basis of the optimization of theobjective function in (28)

$\begin{matrix}{{{J_{k}^{d} = {\sum\limits_{n = 0}^{k}{\lambda_{k - n}^{d}{{{{\overset{\_}{w}}^{H}{\overset{\_}{\psi}}_{n}} - a_{n + M_{1}}^{d}}}^{2}}}};}{{\overset{\_}{\psi}}_{n} = \lbrack {z_{n + K_{1}},\ldots\mspace{14mu},z_{n + M_{1}},\ldots\mspace{14mu},z_{n + M_{1} - N_{1}}} \rbrack^{T}}} & (28)\end{matrix}$with respect to the equalizer parameter vector w and results in the RLSalgorithm in (29a, b).ŵ _(k+1) = ŵ _(k)+μ_(d) R _(k) ψ _(k)(a _(k+M) ₁ ^(d) − ŵ _(k) ^(H) ψ_(k))*;   (29a)R _(k)=λ⁻¹ [R _(k−1) −R _(k−1) ψ _(k)( ψ _(k) ^(H) R _(k−1) ψ _(k)+λ)⁻¹ψ _(k) ^(H) R _(k−1) ];k=1,2, . . .   (29b)In (29b) the matrix R_(k) at time k=0 may be initialized by a diagonalmatrix ε_(R)I_(N) for some small positive scalar ε_(R) with I_(N)denoting the (N×N) identity matrix. Based on the optimization of thefunction J_(k) ^(d), the first correction signal vector w _(k) ^(c) ¹ in(27b) may be modified to arrive at the alternative equalizer parametervector update algorithm in (30)ŵ _(k+1) = ŵ _(k)+μ_(d) ŵ _(k) ^(c) ¹ −μ ŵ _(k) ^(c) ²   (30a)ŵ _(k) ^(c) ¹ =R _(k) ψ _(k)(a _(k+M) ₁ ^(d) − ŵ _(k) ^(H) ψ_(k))*;k=0,1, . . .   (30b)With R_(k) in (30b) updated according to (29b). The algorithm in (30)may result in a faster convergence compared to that in (27).

In various other embodiments of the invention the first correctionsignal vector w _(k) ^(c) ¹ may be based on the one of the quantizedstate algorithms such as the QS1 algorithm given byŵ _(k) ^(c) ¹ =R _(k) ψ _(k) ^(q)(a _(k+M) ₁ ^(d) − ŵ _(k) ^(H) ψ_(k))*  (31a)R _(k) ^(q)=λ⁻¹ [R _(k−1) ^(q) −R _(k−1) ^(q) ψ _(k) ^(q)( ψ _(k) ^(H) R_(k−1) ^(q) ψ _(k) ^(q)+λ)⁻¹ ψ _(k) ^(H) R _(k−1) ^(q) ];k=0,1, . . .  (31b)The vector ψ _(k) ^(q) is obtained by replacing both the real andimaginary components of the various components of the vector ψ _(k) withthe 1 bit quantized versions. The i^(th) component of ψ _(k) ^(q) isgiven by (31c).ψ_(k,i) ^(q)=sgn(Re(ψ_(k,i)))+jsgn(Im(ψ_(k,i)));j=√{square root over(−1)};i=−N ₁, . . . ,0, . . . ,N ₁  (31c)In (31c) sgn(x) for x real is the signum function defined in (22), andRe(z) and Im(z) denote the real and imaginary components of z for anycomplex variable z.

Referring to FIG. 1, the output z_(k), for any integer k, of the channelgain normalizer block 7 in FIG. 1 may be expressed asz _(k) =y _(k) +n _(k);  (32a)

$\begin{matrix}{{{y_{k} = {\sum\limits_{i = {- M_{1}}}^{M_{1}}{h_{i}^{*}a_{k - 1}}}};}{{k = 0},1,\ldots}} & ( {32b} )\end{matrix}$where h_(i), −M₁, . . . , 0, . . . , M₁, are the components of thechannel impulse response vector h related to the vector h ^(c) via thechannel gain G_(k) ^(m) shown in FIG. 5. From (32a,b) an exponentiallydata weighted least squares algorithm for the estimate of the channelimpulse response vector ĥ _(k) may be obtained by minimizing theoptimization index θ_(1,k) with respect to h where

$\begin{matrix}{{{J_{1,k} = {\sum\limits_{m = 0}^{k}{\lambda^{k - m}{{z_{m} - {{\overset{\_}{h}}^{H}{\overset{\_}{x}}_{m}}}}^{2}}}};}{{{\overset{\_}{x}}_{m} = \lbrack {a_{m + M_{1}},{\ldots\mspace{14mu} a_{m}},{\ldots\mspace{14mu} a_{m + M_{1}}}} \rbrack^{T}};}{{k = 0},1,\ldots}} & (33)\end{matrix}$In (33) the exponential data weighting coefficient λ, is a constanttaking values in the interval 0<λ≦1. The gradient of θ_(1,k) withrespect to h is evaluated as

$\begin{matrix}{\frac{\partial J_{1,k}}{\partial\overset{\_}{h}} = {{\sum\limits_{m = 0}^{k}{\lambda^{k - m}{\overset{\_}{x}}_{m}z_{m}}} - {\sum\limits_{m = 0}^{k}{\lambda^{k - m}{\overset{\_}{h}}^{H}{\overset{\_}{x}}_{m}{\overset{\_}{x}}_{m}^{H}}}}} & (34)\end{matrix}$The exponential data weighted least squares (LS) algorithm is obtainedby setting the gradient in (34) equal to zero and is given by

$\begin{matrix}{{\hat{\overset{\_}{h}}}_{k} = {P_{k}( {\sum\limits_{m = 0}^{k}{\lambda^{k - m}{\overset{\_}{x}}_{m}z_{m}^{*}}} )}} & ( {35a} ) \\{P_{k} = \lbrack {P_{k - 1}^{- 1} + {\sum\limits_{m = 0}^{k}{\lambda^{k - m}{\overset{\_}{x}}_{m}{\overset{\_}{x}}_{m}^{H}}}} \rbrack^{- 1}} & ( {35b} )\end{matrix}$In (35b) P⁻¹ ⁻¹=εI for some small positive scalar ε and with I denotingthe identity matrix. Alternatively, the use of the matrix inversionlemma yields the following recursive least squares (RLS) algorithmĥ _(k) = ĥ _(k−1) +P _(k) x _(k) e _(k) *;e _(k)=(z _(k) −z_(k));{circumflex over (z)} _(k) = ĥ _(k−1) ^(H) x _(k);  (36a)P _(k)=λ⁻¹ [P _(k−1) −P _(k−1) x _(k)(λ+ x _(k) ^(H) P _(k−1) x _(k))⁻¹x _(k) ^(H) P _(k−1) ];k=0,1, . . .   (36b)In (36) the estimate ĥ ⁻¹ may be set to some a-priori estimate, forexample, ĥ ⁻¹=[0 . . . 010 . . . 0]^(T) with P⁻¹ selected as in (35b).In one of the preferred embodiment of the invention the RLS algorithm(36) is used for the estimation of h.

In an alternative embodiment of the invention, an exponentially dataweighted Kaman filter algorithm may be used. The Kaman filter minimizesthe conditional error variance in the estimate of the channel impulseresponse given by E[∥ h− ĥ∥²/z₀, z₁, . . . , z_(k)], where E denotes theexpected value operator. The exponentially data weighted Kaman filteralgorithm is given byĥ _(k) = ĥ _(k−1) +K _(k)(z _(k) − ĥ _(k−1) ^(H) x _(k))*  (37a)K _(k) =P _(k−1) x _(k)( x _(k) ^(H) P _(k−1) x _(k)+λr_(k))⁻¹  (37b)P _(k)=λ⁻¹ [P _(k−1) −P _(k−1) x _(k)( x _(k) ^(H) P _(k−1) x _(k) +λr_(k))⁻¹ x _(k) ^(H) P _(k−1)]  (37c)The equations (37a)-(37c) may be initialized at k=0 with similarinitialization as for the RLS algorithm of (36). Equations (37a) and(37b) may be combined into the following equivalent formĥ _(k) = ĥ _(k−1) +P _(k) r _(k) ⁻¹ x _(k)(z _(k) − ĥ _(k−1) ^(H) x_(k))*  (37d)In equations (37b)-(37d), r_(k) r_(k)=2σ² denotes the variance of thenoise n_(k) in (32a) equal to the noise n_(k) ^(c) normalized by themodified channel gain G_(k) ^(m).

In another embodiment of the invention, one of the class of quantizedstate algorithms may be used for the estimation of h. The quantizedstate algorithms possess advantages in terms of the computationalrequirements. For example, the quantized state QS1 algorithm is given byĥ _(k) = ĥ _(k−1) +P _(k) ^(q) x _(k) ^(q)(z _(k) − ĥ _(k−1) ^(H) x_(k))*  (38a)P _(k) ^(q)=λ⁻¹ [P _(k−1) ^(q) −P _(k−1) ^(q) x _(k) ^(q)( x _(k) ^(H) P_(k−1) ^(q) x _(k) ^(q)+λ)⁻¹ x _(k) ^(H) P _(k−1) ^(q) ];k=0,1, . . .  (38b)where in (38) x ^(q) is obtained from x by replacing both the real andimaginary components of each component of x by their respective signstaking values +1 or −1. Multiplication of x ^(q) by the matrix P^(q) in(38b) requires only additions instead of both additions andmultiplications, thus significantly reducing the computationalrequirements.Referring to FIG. 1, in the blind mode equalizer system 80, the channelinput a_(k) appearing in the state vector x _(k) in (34)-(38) isreplaced by the detected symbol a_(k) ^(d). The state vector x _(k) inthe equations (34)-(38) is replaced by its estimate given by{circumflex over (x)} _(k) =[a _(k+M) ₁ ^(d) , . . . ,a _(k) ^(d) , . .. ,a _(k−M) ₁ ^(d)]^(T)  (39)The resulting modified RLS algorithm is given byĥ _(k) = ĥ _(k−1) P _(k) {circumflex over (x)} _(k)(z _(k) − ĥ _(k−1)^(H) {circumflex over (x)} _(k))*  (40a)P _(k)=λ⁻¹ [P ^(k−1) −P _(k−1) {circumflex over (x)} _(k)(λ+ {circumflexover (x)} _(k) ^(H) P _(k−1) {circumflex over (x)} _(k))⁻¹ {circumflexover (x)} _(k) ^(H) P _(k−1) ];k=0,1, . . .   (40b)

In one of the various preferred embodiments of the invention, themodified RLS algorithm (40a)-(40b) is used for the estimation of thechannel impulse response h. In various alternative embodiments the Kamanfilter algorithms in (37) or the quantized state algorithm in (38) withthe state vector x _(k) replaced with the estimate {circumflex over (x)}_(k) may be used for the estimation of the channel impulse response h.

FIG. 7 shows the block diagram of the channel estimator block 440 ofFIG. 6. Referring to FIG. 7, the detected symbol 12 a_(k+M) ₁ ^(d) fromthe output of the decision device 11 is input to a cascade of 2M₁ delayelements 510 generating the 2M₁ delayed versions 512 a_(k+M) ₁ ⁻¹ ^(d),. . . , a_(k−M) ₁ ^(d) at the outputs of the delay elements. Thedetected symbol a_(k+M) ₁ and its 2M₁ delayed versions 512 a_(k+M) ₁ ⁻¹,. . . , a_(k−M) ₁ are input to the M=2M₁+1 hm multipliers 514 hm₁, . . ., hm_(M). The M hm multipliers 514 are inputted with the conjugates 518of the M components 516 ĥ_(−M) ₁ _(,k−1), . . . , ĥ_(0,k−1), . . . ,ĥ_(M) ₁ _(,k−1) of the channel impulse response vector ĥ_(k−1) providedby the conjugate blocks 517. The M hm multipliers 514 multiply thedetected symbols a_(k+M) ₁ ^(d), . . . , a_(k−M) ₁ ^(d) by therespective components ĥ_(−M) ₁ _(,k−1), . . . , ĥ_(0,k−1), . . . , ĥ_(M)₁ _(,k−1) of the channel impulse response vector ĥ _(k−1). The outputsof the M hm multipliers 514 are inputted to the summer 575 that providesthe sum of the inputs representing the predicted value 576 {circumflexover (z)}_(k) of the normalized channel output z_(k) at the summeroutput 576. The normalized channel output 436 z_(k) and the predictedvalue 576 {circumflex over (z)}_(k) are input to the adder 578 thatprovides the prediction error signal 579 e_(k) ^(h)=z_(k)−{circumflexover (z)}_(k) at the output of the adder. The error signal 579 e_(h)^(k) is inputted to the conjugate block 580, the output of 581 of theconjugate block 580 is multiplied by a positive scalar μ_(h) in themultiplier 583. The output 584 of the multiplier 583 is input to the Mweight correction multipliers 526 hcm₁, . . . , hcm_(N) wherein e_(k)^(h)* multiplies the M components K_(−M) ₁ _(,k), . . . , K_(0,k), . . ., K_(M) ₁ _(,k) of the gain vector 548 K_(k) provided by the vector toscalar converter 560. The outputs of the hcm₁, . . . , hcm_(M)multipliers 526 are input to the N hca adders 518 hca₁, . . . , hca_(M).

Referring to FIG. 7, the M hca adders 518 are inputted with the Mcomponents ĥ_(−M) ₁ _(,k−1), . . . , ĥ_(0,k−1), . . . , ĥ_(M) ₁ _(,k−1)of the channel impulse response vector ĥ _(k−1) at the outputs of the Mdelay elements 520 and with the outputs 522 of the M hcm multipliers526. The hca adders 518 add the M channel impulse response vectorcomponents ĥ_(−M) ₁ _(,k−1), . . . , ĥ_(0,k−1), ĥ_(M) ₁ _(,k−1) to thecorresponding M outputs 522 of the hcm₁, . . . , hcm_(M) multipliers 526providing the updated version of the M components of the channel impulseresponse vector ĥ _(k) at the outputs of the M hca adders 518. Theoutputs 524 of the M hca adders 518 are connected to the inputs of the Mdelay elements 520 with the outputs of the delay elements connected tothe M conjugate blocks 517. The estimate of the channel impulse responsevector may be initialized at k=−1 by the vector δ_(M) ₁ _(,M) ₁ =[0 . .. 010 . . . 0]^(T).

Referring to FIG. 7, the detected symbol 12 a_(k+M) ₁ ^(d) and itsvarious delayed versions 512 a_(k+M) ₁ ⁻¹ ^(d), . . . , a_(k−M) ₁ ^(d)are input to the scalar to vector converter 530 providing the channelstate vector 532 {circumflex over (x)} _(k)=[a_(k+M) ₁ ^(d), . . . ,a_(k) ^(d) . . . , a_(k−M) ₁ ^(d)]^(T) at the output of the scalar tovector converter 530. Referring to FIG. 7, the channel state vector 530{circumflex over (x)} _(k) is input to the gain update block 550 thatprovides the gain vector 548 K(k) to the vector to scalar converter 560.Referring to FIG. 7, the channel state vector 530 {circumflex over (x)}_(k) and the matrix 545 P_(k−1) are input to the matrix P_(k) updateblock 542 that evaluates the updated matrix 543 P_(k) according toequation (36b) and provides the updated matrix 543 P_(k) to the delay544. The output 545 of the delay 544 equal to P_(k−1) is inputted to thematrix P_(k) update block 542. The matrix P_(k) update block 542 isinitialized with input 546 P⁻¹=εI_(M), where ε is some positive numberand I_(M) is the M×M identity matrix. The matrix 543 P_(k) and thechannel state vector 532 {circumflex over (x)} _(k) are input to thematrix multiplier 541 that provides the gain vector 548 K_(k)=P_(k){circumflex over (x)} _(k) at the output. The gain vector 548 K_(k) isinputted to the vector to scalar converter 560.

With the channel impulse response vector h ^(T)=[h_(−M) ₁ . . . h⁻¹h₀h₁. . . h_(M) ₁ ] of length M=2M₁+1, and w ^(T)=[w_(−N) ₁ , . . . , w⁻¹,w₀, w₁, . . . , w_(N) ₁ ] of length N=2N₁+1, the composite systemcomprised of the cascade of the channel and the equalizer has an impulseresponse g ^(T) of length K=N+M−1 with K=2K₁+1, K₁=N₁+M₁−1g=[g _(−K) ₁ . . . g ⁻¹ g ₀ g ₁ . . . g _(K) ₁ ]^(T)  (41)The elements of the vector g are obtained by the discrete convolution ofthe sequences {h_(−M) ₁ , . . . , h⁻¹, h₀, h₁, . . . , h_(M) ₁ } and{w⁻¹, . . . , w⁻¹, w₀, w₁, . . . , w_(N) ₁ }. For simplicity ofnotations, the sequences are also represented as vectors h and wrespectively with the similar notations for the other sequences. Theconvolution operation can also be expressed in the following matrixvector formg=H w   (42)With N₁>M₁ as is usually the case, the K×N matrix H in (42) may bewritten in the following partitioned form

$\begin{matrix}{H = \begin{bmatrix}H_{1} & \; & O_{M \times {({N - M})}} \\\; & H_{3} & \; \\O_{M \times {({N - M})}} & \; & H_{2}\end{bmatrix}} & (43)\end{matrix}$In (43) O_(M×(N−M)) denotes M×(N−M) matrix with all its elements equalto zero and

$\begin{matrix}{H_{1} = \begin{bmatrix}h_{- M_{1}} & 0 & 0 & \ldots & 0 \\h_{{- M_{1}} + 1} & h_{- M_{1}} & 0 & \ldots & 0 \\\; & \ldots & \ldots & \ldots & \; \\h_{M_{1}} & \ldots & h_{0} & \ldots & h_{- M_{1}}\end{bmatrix}} & ( {44a} ) \\{H_{2} = \begin{bmatrix}h_{M_{1}} & \ldots & \ldots & h_{0} & \ldots & h_{- M_{1}} \\0 & h_{M_{1}} & \ldots & h_{0} & \ldots & h_{{- M_{1}} + 1} \\\; & \; & \ldots & \ldots & \ldots & \mspace{11mu} \\0 & 0 & \ldots & \ldots & 0 & h_{M_{1}}\end{bmatrix}} & ( {44b} ) \\{H_{3} = \begin{bmatrix}\; & 0 & h_{M_{1}} & \ldots & h_{0} & \ldots & h_{- M_{1}} & {\;\underset{\underset{00\mspace{14mu}\ldots\mspace{14mu} 0}{︷}}{N - M - 1}} \\0 & 0 & h_{M_{1}} & \ldots & h_{0} & \ldots & h_{- M_{1}} & {0\mspace{14mu}\ldots\mspace{14mu} 0} \\\; & \; & \; & \ldots & {\;\ldots} & {\ldots\;} & \; & \; \\\underset{\underset{N - M - 1}{︸}}{00\mspace{14mu}\ldots\mspace{14mu} 0} & h_{M_{1}} & \ldots & h_{0} & \ldots & \; & h_{- M_{1}} & 0\end{bmatrix}} & ( {44c} ) \\{H = \begin{bmatrix}h_{- M_{1}} & 0 & \ldots & \ldots & \ldots & \ldots & \ldots & 0 \\h_{{- M_{1}} + 1} & \; & h_{- M_{1}} & 0 & \ldots & \ldots & \ldots & 0 \\\; & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \; \\\underset{\underset{N_{1} - M_{1}}{︸}}{00\mspace{14mu}\ldots\mspace{14mu} 0} & h_{M_{1}} & \; & \ldots & h_{0} & \ldots & h_{M_{1} - 1} & \underset{\underset{N_{1} - M_{1}}{︸}}{00\mspace{14mu}\ldots\mspace{14mu} 0} \\\; & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \; \\0 & 0 & \ldots & \ldots & \ldots & 0 & h_{M_{1}} & h_{M_{1} - 1} \\0 & 0 & \; & \ldots & \ldots & 0 & 0 & h_{M_{1}}\end{bmatrix}} & ( {44d} )\end{matrix}$

The matrix H in (44d) can be appropriately modified for the case ofN₁<M₁. For the case of known channel impulse response h, the equalizerparameter vector w can be selected so that the impulse response of thecomposite system g ^(T) given by (42) is equal to δ _(K) ₁ _(,K) ₁ whichis defined for any pair of positive integers K₁, K′₁ as

$\begin{matrix}{{\overset{\_}{\delta}}_{K_{1},K_{1}^{\prime}}^{T} = \begin{bmatrix}\underset{\underset{K_{1}}{︸}}{00\mspace{14mu}\ldots\mspace{14mu} 0} & 1 & \underset{\underset{K_{1}^{\prime}}{︸}}{00\mspace{14mu}\ldots\mspace{14mu} 0}\end{bmatrix}} & (45)\end{matrix}$For the case of non singular matrix H, this can be achieved by theselection of w byw=H ⁻¹ δ; δ= δ _(K) ₁ _(,K) ₁   (46)However, for the more general case the equalizer parameter vector w maybe selected so as to minimize some measure of the difference between gand the unit vector δ. Thus the objective function J_(L) _(i) to beminimized is given byJ _(L) _(i) =∥H w− δ∥ _(L) _(i)   (47)where ∥ ∥_(L) _(i) denotes the L_(i) norm. For example, the L₁ norm isgiven by

$\sum\limits_{j = {- K_{1}}}^{K_{1}}{( {g_{j} - \delta_{j}} )}$with δ_(j) denoting the jth component of the vector δ. The L_(∞) norm isgiven by

$\max\limits_{j}{{{g_{j} - \delta_{j}}}.}$Computationally the Euclidean norm L₂ is most convenient and is given by

$\begin{matrix}\begin{matrix}{= J_{2}} \\{= J_{L_{2}}} \\{= {\sum\limits_{j = {- K_{1}}}^{K_{1}}{( {{H\overset{\_}{w}} - \overset{\_}{\delta}} )_{j}}^{2}}} \\{= {\sum\limits_{j = {- K_{1}}}^{K_{1}}{( {g_{j} - \delta_{j}} )}^{2}}}\end{matrix} & (48)\end{matrix}$Equivalently the optimization function in (48) may be expressed in thefollowing equivalent formJ ₂=(H w /− δ)^(H)(H w /− δ)  (49)The gradient of θ₂ with respect to the equalizer parameter vector w isevaluated as

$\begin{matrix}{\frac{\partial J_{2}}{\partial\overset{\_}{w}} = {H^{T}( {{H\overset{\_}{w}} - \overset{\_}{\delta}} )}^{*}} & (50)\end{matrix}$An iterative algorithm to minimize the objective function θ₂ is given byŵ _(k+1) = ŵ _(k) −μH ^(T)( ĝ _(k)− {circumflex over (δ)})*; ĝ _(k) =H ŵ_(k) ;k=0,1, . . .   (51)with an appropriate initialization for ŵ ₀. As an example, ŵ ₀ may beselected equal to the unit vector δ _(N) ₁ _(,N) ₁ of length (2N₁+1).

More generally the optimization function may be selected as

$\begin{matrix}{J_{2} = {{{\kappa_{1}J_{L_{2}}} + {\kappa_{2}J_{L_{4}}}} = {{\kappa_{1}{\sum\limits_{j = {- K_{1}}}^{K_{1}}{( {g_{j} - \delta_{j}} )}^{2}}} + {\kappa_{2}{\sum\limits_{j = {- K_{1}}}^{K_{1}}{( {g_{j} - \delta_{j}} )}^{4}}}}}} & (52)\end{matrix}$In (52) κ₁ and κ₂ are some positive constants determining the relativeweights assigned to J_(L) ₂ and J_(L) ₄ respectively. Differentiation ofJ_(L) ₄ with respect to the equalizer parameter w_(i) yields

$\begin{matrix}\begin{matrix}{\frac{\partial J_{L_{4}}}{\partial w_{i}} = {2{\sum\limits_{j = {- K_{1}}}^{K_{1}}{{( {g_{j} - \delta_{j}} )}^{2}( {g_{j} - \delta_{j}} )^{*}\frac{\partial g_{j}}{\partial w_{i}}}}}} \\{= {2{\sum\limits_{j = {- K_{1}}}^{K_{1}}{H_{ji}{( {g_{j} - \delta_{j}} )}^{2}( {g_{j} - \delta_{j}} )^{*}}}}}\end{matrix} & (53)\end{matrix}$From (53), the gradient vector of J_(L) ₄ with respect to the equalizerparameter vector w is given by

$\begin{matrix}{\frac{\partial J_{L_{4}}}{\partial\overset{\_}{w}} = {{2{H^{T}\lbrack {{( {\overset{\_}{g} - \overset{\_}{\delta}} )}^{2}{\square( {\overset{\_}{g} - \overset{\_}{\delta}} )^{*}}} \rbrack}} \equiv {2H^{T}{\overset{\_}{g}}^{c}}}} & (54)\end{matrix}$In (54) the n^(th) power of any vector x for any real n is defined astaking the component wise n^(th) power of the elements of the vector x,| x| denotes component wise absolute value and □ denotes component wisemultiplication, and thus the result of vector operations in (54) is avector of the same length as that of x for any vector x. From (54) amore general version of the iterative algorithm to minimize theobjective function in (52) is given byŵ _(k+1) = ŵ _(k) −μH ^(T)[( ĝ _(k)− δ)*+κ|( ĝ _(k)−δ)|²□( ĝ _(k)− δ)]*;ĝ _(k) =H ŵ _(k)  (55a)ŵ _(k+1) = ŵ _(k) −μH ^(T){[ 1+κ|( ĝ _(k)−δ)|²]□( ĝ _(k)− δ)*}; ĝ _(k)=H ŵ _(k) ;k=0,1, . . .   (55b)In (55b) 1 denotes a vector with all its elements equal to 1 and itslength equal to that of ĝ _(k). In (55a,b) μ and κ are some positiveconstants that are sufficiently small to ensure the convergence of thealgorithm in (55).

In one of the various embodiments of the BMAEHS equalizer of theinvention, the second correction signal vector ŵ _(k) ^(c) ² is selectedasŵ _(k) ^(c) ² =H ^(T){[ 1+κ|( ĝ _(k)− δ)²]□( ĝ _(k)− δ)*}; ĝ _(k) =H ŵ_(k) ;k=0,1, . . .   (56)In (56) Ĥ_(k) is given by (44d) with h_(i) replaced by its estimateĥ_(i,k) for i=M₁, . . . , 0, . . . , M₁. In various other embodiments ofthe invention, the second correction signal vector ŵ _(k) ^(c) ² may beobtained from the optimization of the θ₂ in (52) and given byŵ _(k) ^(c) ² =Ĥ _(k) ^(T)[( ĝ _(k)− δ)+κ|( ĝ _(k)− δ)|²□( ĝ _(k)− δ)*];ĝ _(k) =Ĥ _(k) ŵ _(k) ;k=0,1, . . .   (57)

FIG. 8 shows the block diagram of the correction signal generator 450 ofFIG. 6 that generates the second correction signal vector 452 ŵ _(k) ²according to (51). Referring to FIG. 8, the estimate of the channelimpulse response vector 442 ĥ _(k) is input to the correction signalgenerator 450. As shown in the FIG. 8, the channel impulse responsevector 442 ĥ _(k) is input to the matrix Ĥ_(k) collator 620 that formsmatrix 622 Ĥ_(k) according to equation (44) with h, replaced by ĥ_(i)for i=M₁, . . . 0 . . . , M₁. The matrix 622 Ĥ_(k) and the equalizerparameter vector 432 ŵ _(k) are input to the matrix multiplier 624 thatprovides the product ĝ _(k=Ĥ) _(k) ŵ _(k) at the matrix multiplieroutput 626. The product 626 ĝ _(k) and the vector 610 δ _(K) ₁ _(,K) ₁=[0 . . . 010 . . . 0] are inputted to the adder 630 that provides thedifference 632 ( ĝ _(k)− δ _(K) ₁ _(,K) ₁ ) to the conjugate block 635.The output 638 of the conjugate block 635 is inputted to the matrixmultiplier 640. The matrix 622 Ĥ_(k) is input to the transpose block 642that provides the matrix 644 Ĥ_(k) ^(T) at the output. The matrix 644Ĥ_(k) ^(T) is inputted to the matrix multiplier 640 that multiplies thematrix 644 Ĥ_(k) ^(T) by 638 ( ĝ _(k)−δ_(K) ₁ _(,K) ₁ ) generating thesecond correction vector 452 ŵ _(k) ^(c) ² at the matrix multiplieroutput.

From the definition of the matrix H in (44), the vector ĝ _(k) in (51)and (55) can also be obtained by the convolution of the channel impulseresponse h with the equalizer parameter vector ŵ _(k). Similarly the premultiplication by H^(T) in (51) can be evaluated by the convolution of h^(I) with ( ĝ _(k)− δ) and discarding (2M−2) elements from the resultingvector of size K+M−1=N+2M−2, more specifically (M−1) elements arediscarded from each end of the resulting vector, where h ^(I) is thevector obtained by reversing the order of the elements in h, i.e.,h ^(I) =[h _(M) ₁ . . . h ₁ h ₀ h ⁻¹ . . . h _(−M) ₁ ]^(T)  (58)An equivalent form for the update of the equalizer parameter vector ŵ_(k) is given by{circumflex over (w)} _(k+1)= {circumflex over (w)} _(k) −μTr{ h ^(I)

[ h

{circumflex over (w)} _(k)− δ]*}  (59a){circumflex over (w)} _(k+1)= {circumflex over (w)} _(k)−μTr{ h ^(I)

h

{circumflex over (w)} _(k)}*+μ h ^(Ie) ;k=0,1, . . .   (59b)In (59) the operator Tr denotes the truncation of the vector to length Nby deleting (M−1) elements from each side of the vector appearing in itsargument. In (59b) h ^(Ie) is the vector obtained from h ^(I). byappending (N₁−M₁) zeros to each side of h ^(I) with h ^(Ie)=[0 . . . 0 h^(IT)0 . . . 0]^(T). Similarly the convolution version of the algorithmin (55) is given by{circumflex over (w)} _(k+1)= {circumflex over (w)} _(k)−μTr{ h ^(I)

[( {circumflex over (g)} _(k)− δ)*+κ {circumflex over (g)} ^(c)]}  (60a){circumflex over (g)} _(k)= h

{circumflex over (w)} _(k); {circumflex over (g)} _(k) ^(c)=|({circumflex over (g)} _(k)− δ)|²□( {circumflex over (g)} _(k)−δ)*;k=0,1, . . .   (60b)In various alternative embodiments of the invention, second correctionsignal vector w _(k) ^(c) ² may be generated by (61) as{circumflex over (w)} _(k) ^(c) ² =Tr{ {circumflex over (h)} _(k) ^(I)

[( {circumflex over (g)} _(k)− δ)*+κ {circumflex over (g)}^(c)]};  (61a){circumflex over (g)} _(k)= {circumflex over (h)} _(k)

{circumflex over (w)} _(k); {circumflex over (g)} ^(c)=|( {circumflexover (g)} _(k)− δ)|²□( {circumflex over (g)} _(k)− δ)*;k=0,1, . . .  (61b)In (61a) ĥ _(k) ^(I) is obtained from (58) after replacing h_(i) withĥ_(i,k) for i=−M₁, . . . , 0, M₁.

In order to minimize the impact of the equalizer on the input noisevariance 2σ², a term proportional to ∥ w∥² may be added to theoptimization function in (52) with the resulting objective functiongiven by

$\begin{matrix}{J_{2} = {{\kappa_{1}{\sum\limits_{j = {- K_{1}}}^{K_{1}}{( {g_{j} - \delta_{j}} )}^{2}}} + {\kappa_{2}{\sum\limits_{j = {- K_{1}}}^{K_{1}}{( {g_{j} - \delta_{j}} )}^{4}}} + {\kappa_{3}2\sigma^{2}{\overset{\_}{w}}^{2}}}} & (62)\end{matrix}$In (62) the product 2σ²∥ w∥² is the noise variance at the equalizeroutput and κ₃ determines the relative weighting given to power of theresidual inter symbol interference (ISI) I_(s). The ISI power isproportional to the summation in the first term on the right hand sideof (61) and is given by

$\begin{matrix}{\sigma_{I}^{2} = {{E\lbrack {I_{s}}^{2} \rbrack} = {{E\lbrack {a_{k}}^{2} \rbrack}{\sum\limits_{j = {- K_{1}}}^{K_{1}}{( {g_{j} - \delta_{j}} )}^{2}}}}} & (63)\end{matrix}$The power of the total distortion at the output of the equalizer isgiven by

$\begin{matrix}\begin{matrix}{\sigma_{t}^{2} = {{E\lbrack {I_{s}}^{2} \rbrack} + {2\sigma^{2}{\overset{\_}{w}}^{2}}}} \\{= {{{E\lbrack {a_{k}}^{2} \rbrack}{\sum\limits_{j = {- K_{1}}}^{K_{1}}{( {g_{j} - \delta_{j}} )}^{2}}} + {2\sigma^{2}{\overset{\_}{w}}^{2}}}}\end{matrix} & (64)\end{matrix}$and to minimize the total distortion σ_(t) ², the constants κ₁ and κ₃are related by κ₁=E[|a_(k)|²]κ₃. With the modified optimization functionin (62), the iterative algorithm in (60) is modified to{circumflex over (w)} _(k+1)= {circumflex over (w)} _(k)−μTr{ h ^(I)

[( {circumflex over (g)} _(k)− δ)*+κ {circumflex over (g)} _(k)^(c)]}−μ₀ {circumflex over (w)} _(k)*  (65a){circumflex over (g)} _(k)= h

{circumflex over (w)} _(k); {circumflex over (g)} ^(c)=|( {circumflexover (g)} _(k)− δ)|²□( {circumflex over (g)} _(k)− δ)*;k=0,1, . . .  (65b)In (65) the parameter μ₀ with 0≦μ₀<1, is determined by the relativeweight κ₃. In various alternative embodiments of the invention, thesecond correction signal vector w _(k) ^(c) ² may be generated by (66)as{circumflex over (w)} _(k) ^(c) ² =Tr{ {circumflex over (h)} _(k) ^(I)

[( {circumflex over (g)} _(k)− δ)*+κ {circumflex over (g)} _(g)^(c)]}+(μ₀/μ) {circumflex over (w)} _(k)*  (66)In (66) ĝ _(k) and ĝ _(k) ^(c) are given by (61b).

The convolution operation in the iterative algorithms (59), (60) and(65) can be performed equivalently in terms of the discrete Fouriertransform (DFT) or the fast Fourier transform (FFT) operations. The FFToperation results in a circular convolution, hence for properconvolution operation the individual vectors to be convolved are zeropadded with an appropriate number of zeros. Also the FFT of h ^(I) canbe related to the FFT of h if a zero is appended at the beginning of thevector h. Therefore, a vector h ^(e) of length (N+M+2) is defined by

$\begin{matrix}{{\overset{\_}{h}}^{e} = \lbrack {0h_{{- M_{1}}\mspace{11mu}}\ldots\mspace{14mu} h_{- 1}h_{0}h_{1}\mspace{14mu}\ldots\mspace{14mu} h_{M_{1}}\underset{\underset{N + 1}{︸}}{00\mspace{14mu}\ldots\mspace{14mu} 0}} \rbrack^{T}} & (67)\end{matrix}$Similarly a vector ŵ _(k) ^(e) of length (N+M+2) is defined as

$\begin{matrix}{{\hat{\overset{\_}{w}}}_{k}^{e} = \lbrack {{\hat{w}}_{- N_{1}}\mspace{14mu}\ldots\mspace{14mu}{\hat{w}}_{- 1}{\hat{w}}_{0}{\hat{w}}_{1}\mspace{14mu}\ldots\mspace{14mu}{\hat{w}}_{N_{1}}\underset{\underset{M + 2}{︸}}{00\mspace{14mu}\ldots\mspace{14mu} 0}} \rbrack^{T}} & (68)\end{matrix}$For the sake of notational simplification, the suffix k denoting thetime index has been dropped from the elements of the vector ŵ _(k) ^(e).Leth ^(eF) =F( h ^(e)); ŵ _(k) ^(eF) =F( ŵ _(k) ^(e))  (69)where in (69), the operator Φ denotes the (N+M+2) point discrete Fouriertransform of its argument. For any vector ξ of size N, its DFT is givenbyξ ^(F)=Γ_(N) ξ  (70a)Where Γ_(N) is the N×N matrix given by

$\begin{matrix}{\Gamma_{N} = \begin{bmatrix}\gamma_{0,0} & \gamma_{0,1} & \ldots & \gamma_{0,{N - 1}} \\\gamma_{1,0} & \gamma_{1,1} & \ldots & \gamma_{1,{N - 1}} \\\ldots & \ldots & \ldots & \ldots \\\gamma_{{N - 1},0} & \gamma_{{N - 1},1} & \ldots & \gamma_{{N - 1},{N - 1}}\end{bmatrix}} & ( {70b} ) \\{{{\gamma_{m,n} = {\exp\lbrack {{- {j2\pi}}\;{{mn}/N}} \rbrack}};}{{j = \sqrt{- 1}};}{m,{n = 0},1,\ldots\mspace{14mu},{N - 1}}} & ( {70c} )\end{matrix}$

The discrete Fourier transform in (70) can be implemented by the fastFourier transform algorithm resulting in significant reduction in thenumber of required arithmetic operations. Definingĝ _(k) ^(eF) = h ^(eF)□ ŵ _(k) ^(eF)  (71)with □ denoting the component wise multiplication, then the inversediscrete Fourier transform (IDFT) of ĝ _(k) ^(eF) is given by

$\begin{matrix}\begin{matrix}{{F^{- 1}( {\hat{\overset{\_}{g}}}_{k}^{eF} )} = {\Gamma_{({K + 3})}^{*}{\hat{\overset{\_}{g}}}_{k}^{eF}}} \\{= \lbrack {0{\hat{g}}_{- K_{1}}\mspace{14mu}\ldots\mspace{14mu}{\hat{g}}_{- 1}{\hat{g}}_{0}{\hat{g}}_{1}\mspace{14mu}\ldots\mspace{14mu}{\hat{g}}_{K_{1}}00} \rbrack^{T}} \\{= \lbrack {0{\hat{\overset{\_}{g}}}_{k}00} \rbrack^{T}}\end{matrix} & (72)\end{matrix}$The inverse DFT of ( h ^(eF))*, where * denotes complex conjugate, isgiven by

$\begin{matrix}\begin{matrix}{{F^{- 1}\lbrack ( {\overset{\_}{h}}^{eF} )^{*} \rbrack} = \lbrack {\underset{\underset{({N + 2})}{︸}}{00\mspace{14mu}\ldots\mspace{14mu} 0}h_{M_{1}}\mspace{14mu}\ldots\mspace{14mu} h_{1}h_{0}h_{- 1}\mspace{14mu}\ldots\mspace{14mu} h_{- M_{1}}} \rbrack^{H}} \\{= \lbrack {\underset{\underset{({N + 2})}{︸}}{00\mspace{14mu}\ldots\mspace{14mu} 0}( {\overset{\_}{h}}^{I} )^{H}} \rbrack^{T}}\end{matrix} & (73)\end{matrix}$From (71)-(73) the IDFT of the product of ĝ _(k) ^(eF) and ( h ^(eF)) is

$\begin{matrix}\begin{matrix}{{\hat{\overset{\_}{w}}}^{pe} \equiv \lbrack {F^{- 1}\{ {{\overset{\_}{h}}^{eF}{\square{\hat{\overset{\_}{w}}}_{k}^{eF}}{\square( {\overset{\_}{h}}^{eF} )^{*}}} \}} \rbrack^{*}} \\{= \lbrack {{\hat{w}}_{- N_{1}}^{p}\mspace{14mu}\ldots\mspace{14mu}{\hat{w}}_{- 1}^{p}{\hat{w}}_{0}^{p}{\hat{w}}_{1}^{p}\mspace{14mu}\ldots\mspace{14mu}{\hat{w}}_{N_{1}}^{p}\underset{\underset{M + 2}{︸}}{{**\ldots}*}} \rbrack^{T}}\end{matrix} & (74)\end{matrix}$In (74) the symbol * on the right hand side of the equation denotes theelements that are irrelevant and the remaining elements are the same asthe ones obtained by the conjugate of the convolution of h, ŵ _(k), andh ^(I) and deleting (M−1) elements from each side of the resultingvector, that is,Tr₁( h

ŵ _(k)

h ^(I))*=[ŵ_(−N) ₁ ^(p) . . . ŵ₀ ^(p) . . . ŵ_(N) ₁ ^(p)]^(T)  (75)The truncation operation Tr_(i) comprised of deleting (M−1) elementsfrom each side of the vector in its argument on the left hand side of(75) is equivalent to deleting the last (M+2) elements from the vectoron the right hand side of (74). From (74)-(75), a parameter updatealgorithm equivalent to (65a) for the case of κ=0 is given by

$\begin{matrix}{{{\hat{\overset{\_}{w}}}_{k + 1} = {{\hat{\overset{\_}{w}}}_{k} - {\mu\;{Tr}_{2}\{ {F^{- 1}\lbrack {{\hat{\overset{\_}{w}}}_{k}^{eF}{\square{{\overset{\_}{h}}^{eF}}^{2}}} \rbrack} \}^{*}} + {\mu\;{\overset{\_}{h}}^{Ie}} - {\mu_{0}{\hat{\overset{\_}{w}}}_{k}^{*}}}}{where}} & (76) \\{{\overset{\_}{h}}^{Ie} = \lbrack {\underset{\underset{N_{1} - M_{1\;}}{︸}}{00\mspace{14mu}\ldots\mspace{14mu} 0}h_{M_{1}}\mspace{14mu}\ldots\mspace{14mu} h_{1}h_{0}h_{- 1}\mspace{14mu}\ldots\mspace{14mu} h_{- M_{1}}\underset{\underset{N_{1} - M_{1}}{︸}}{00\mspace{14mu}\ldots\mspace{14mu} 0}} \rbrack^{T}} & (77)\end{matrix}$In (76) the truncation operation Tr₂ is comprised of discarding the last(M+2) elements from the vector in its argument and in (77) h ^(Ie) isobtained by appending (N₁−M₁) zeros on both sides of h. The parameterupdate in (76) requires 2 FFT and 1 IFFT operations.

For the more general case of κ≠0 the parameter update algorithm is givenby

$\begin{matrix}{{\hat{\overset{\_}{w}}}_{k + 1} = {{\hat{\overset{\_}{w}}}_{k} - {\mu\;{Tr}_{2}\{ {F^{- 1}\lbrack {( {\overset{\_}{h}}^{eF} )^{*}{\square\lbrack {{\hat{\overset{\_}{g}}}_{k}^{eF} - {\overset{\_}{\delta}}^{F} + {\kappa{\hat{\overset{\_}{g}}}_{k}^{cF}}} \rbrack}} \rbrack} \}^{*}} - {\mu_{0}{\hat{\overset{\_}{w}}}_{k}^{*}}}} & ( {78a} )\end{matrix}$where ĝ _(k) ^(eF) is given by (71) and δ ^(F) is the Fourier transformof δ _(K) ₁ _(+1,K) ₁ ₊₃ given by

$\begin{matrix}{{\overset{\_}{\delta}}_{{K_{1} + 1},{K_{1} + 3}} = \lbrack {\underset{\underset{K_{1} + 1}{︸}}{00\mspace{14mu}\ldots\mspace{14mu} 0}\mspace{25mu} 1\mspace{14mu}\underset{\underset{K_{1} + 3}{︸}}{\mspace{11mu}{00\mspace{14mu}\ldots\mspace{14mu} 0}}} \rbrack^{T}} & ( {78b} )\end{matrix}$and is equal to the (K₁+2)^(th) row of the matrix Γ_(K) defined by (70b)with N replaced by (K+3). In (78a) ĝ _(k) ^(cF) denotes the FFT of [0 ĝ_(k) ^(cT) 00]^(H). In the FFT based implementation, the secondcorrection signal vector w _(k) ^(c) ² may be given by

$\begin{matrix}{{\hat{\overset{\_}{w}}}_{k}^{c_{2}} = {{{Tr}_{2}\{ {F^{- 1}\lbrack {{\hat{\overset{\_}{w}}}^{eF}{\square{{\hat{\overset{\_}{h}}}^{eF}}^{2}}} \rbrack} \}^{*}} - {\hat{\overset{\_}{h}}}_{k}^{Ie} + {( {\mu_{0}/\mu} ){\hat{\overset{\_}{w}}}_{k}^{*}}}} & (79)\end{matrix}$In (79) ĥ ^(eF) is obtained from (69) after replacing h ^(e) by ĥ _(k)^(e), ĥ _(k) ^(Ie) is given by (77) after replacing h_(i) by theestimate ĥ_(i,k) for i=−M₁, . . . , 0, . . . , M₁, and the truncationoperation Tr₂ is comprised of discarding the last (M+2) elements fromthe vector in its argument.

FIG. 9 shows the FFT implementation of the correction signal generator450B of FIG. 6. Referring to FIG. 9, the equalizer parameter vector 432ŵ _(k) is input to the vector to scalar converter 710 that provides theN components 712 ŵ_(−N) ₁ _(,k), . . . , ŵ_(0,k), . . . , ŵ_(N) ₁ _(,k)of the vector ŵ _(k) at the output. The N components 712 ŵ_(−N) ₁ _(,k),. . . , ŵ_(0,k), . . . , ŵ_(N) ₁ _(,k) along with (M+2) zeros are inputto the (K+3) point FFT1 block 720. The FFT1 block 720 evaluates the(K+3) point FFT transform of the inputs 712, 714 and provides the (K+3)outputs 735 ŵ_(0,k) ^(eF), . . . , ŵ_(K+2,k) ^(eF) to the multipliers736 ftm₁, . . . , ftm_(K+3). Referring to FIG. 9, the estimate of thechannel impulse response vector 442 ĥ _(k) is input to the vector toscalar converter 724 that provides the M outputs 726 to the inputs ofthe FFT2 block 730. The other (N+2) inputs 727, 728 of the FFT2 block730 are set equal to 0. The (K+3) outputs 731 of the FFT2 block 730ĥ_(0,k) ^(eF), . . . , ĥ_(0,K+2) ^(eF) are input to the (K+3) modulussquare blocks 732 msq₁, . . . , msq_(K+3). The outputs 733 of the (K+3)modulus square blocks 732 msq₁, . . . msq_(K+3) are connected to theinputs of the respective (K+3) multipliers 736 ftm₁, . . . , ftm_(K+3).The (i+1)^(th) ftm multiplier ftm_(i) multiplies ŵ_(i,k) ^(eF) and|ĥ_(i,k) ^(eF)|² provides the output 737 to the (i+1)^(th) input of the(K+3) point IFFT block 740 for

i=0, 1, . . . , (K+2). The IFFT block 740 evaluates the (K+3) point IFFTof the (K+3) inputs 737. The last (M+2) outputs 749 of the IFFT block740 are discarded.

Referring to FIG. 9, the first 742 (N₁−M₁) and the last 748 (N₁−M₁) ofthe remaining N outputs of the IFFT block 740 denoted by ŵ_(N) ₁ _(−M) ₁_(,k), . . . , ŵ_(N) ₁ _(−M) ₁ _(−1,k), ŵ_(N) ₁ _(+M) ₁ _(+1,k), . . .ŵ_(N−1,k) ^(pe) are inputted to the respective 2(N₁−M₁) inputs of thescalar to vector converter 760. The M components 744 of the IFFT blockŵ_(N) ₁ _(−M) ₁ _(,k), . . . , ŵ_(N) ₁ _(+M) ₁ _(,k) are inputted to theinputs of the M fta adders 746 fta₁, . . . , fta_(M) that subtract thecomplex conjugate 751 of the 726 ĥ_(−M) ₁ _(,k), . . . , ĥ_(0,k), . . ., ĥ_(M) ₁ _(,k) respectively provided by the conjugate block 750 fromthe inputs 744 provided by the IFFT block 740 by the adders 746. Theoutputs 726 ĥ_(M) ₁ _(,k), . . . , ĥ_(0,k), . . . ĥ_(M) ₁ _(,k) of thevector to scalar converter 734 are provided to the conjugate block 750.Referring to FIG. 9, the outputs of the M fta adders are inputted to thescalar to vector converter 760 that provides the vector 761

${\hat{\overset{\_}{w}}}_{k}^{{pc}^{*}} = {{{Tr}\{ {F^{- 1}\lbrack {{\hat{\overset{\_}{w}}}_{k}^{eF}{\square{{\hat{\overset{\_}{h}}}_{k}^{eF}}^{2}}} \rbrack} \}} - {\hat{\overset{\_}{h}}}_{k}^{{Ie}^{*}}}$to the conjugate block 762. The output 764 ŵ _(k) ^(pc) of the conjugateblock 762 is input to the adder 780 that adds (μ₀/μ) ŵ _(k) provided bythe multiplier 766 to 764 ŵ _(k) ^(pc) with the result of the additionequal to the second correction signal vector 452 w _(k) ^(c) ² . Theconjugate of the equalizer parameter vector 432 ŵ _(k) is inputted tothe multiplier 765. The second correction signal vector 452 ŵ _(k) ^(c)² is inputted to the adaptation block 16 of FIG. 6. As in (79) μ and μ₀are small positive scalars and determine the relative weights assignedto the noise and ISI as in ((62)-(65).

In one of the various alternative embodiments of the invention, theequalizer filter 9 in the BMAEHS 60 of FIG. 1 may be selected as thedecision feedback equalizer (DFE) filter. In the decision feedbackequalizer some of the components of the equalizer state vector ψ _(k)are replaced by the detected symbols that are available at the instanceof detecting the present symbol a_(k+M) ₁ ^(d). The equalizer parametervector update algorithm is given byŵ _(k+1) = ŵ _(k)+μ_(d) ŵ _(k) ^(c) ¹ −μ ŵ _(k) ^(c) ² ;  (80a)ŵ _(k) ^(c) ¹ = ψ _(k)(a _(k+M) ₁ ^(d) − ŵ _(k) ^(H) ψ _(k))*;  (80b)ψ _(k) =[z _(k+K) ₁ , . . . ,z _(k+M) ₁ ,a _(k+M) ₁ ⁻¹ ^(d) . . . ,a_(k+M) ₁ _(−N) ₂ ^(d) ];k=0,1, . . .   (80c)In (80) the dimension N of the equalizer parameter vector ŵ _(k) isgiven by N=N₁+N₂+1 with N₂ denoting the number of components of theequalizer parameter state vector that are equal to the previous detectedsymbols. The second correction signal vector ŵ _(k) ^(c) ² in (80a) isgenerated so as to minimize the modeling error in the equalizer andminimizes the norm of the vector that is equal to the difference betweenthe impulse response vector of the cascade of the channel and theequalizer ĝ _(k) ^(m) and the vector δ=[0 . . . 010 . . . 0]^(T) ofappropriate dimension. An expression for the impulse response ĝ _(k)^(m) is obtained by first splitting the equalizer parameter vector ŵ_(k) asŵ _(k) =[ ŵ _(k) ^(+T) ŵ _(k) ^(−T)]^(T)  (81a)ŵ _(k) ⁺ =[ŵ _(−N) ₁ _(,k) , . . . ,ŵ _(0,k)]^(T) ; ŵ _(k) ⁻ =[ŵ _(1,k), . . . ,ŵ _(N) ₂ _(,k)]^(T)  (81b)

For relatively low probability of error in the detection of a_(k), a_(k)^(d)=a_(k) for most of the times and the impulse response vector of thecascade of the channel and the equalizer ĝ _(k) ^(m) may be approximatedby

$\begin{matrix}{{{{\hat{\overset{\_}{g}}}_{k}^{m} = {{\hat{\overset{\_}{g}}}_{k}^{+} + {\hat{\overset{\_}{w}}}_{k}^{- e}}};}{{{\hat{\overset{\_}{g}}}_{k}^{+} = {{\hat{H}}_{k}^{+}{\hat{\overset{\_}{w}}}_{k}^{+}}};}} & ( {82a} ) \\{{\hat{\overset{\_}{w}}}_{k}^{- e} = \lbrack {\underset{\underset{K_{1} + 1}{︸}}{0\mspace{14mu}\ldots\mspace{14mu} 0}{\hat{\overset{\_}{w}}}_{k}^{- T}} \rbrack^{T}} & ( {82b} )\end{matrix}$In (82a) Ĥ_(k) ⁺ is an (M+N₁)×(N₁+1) matrix and is obtained from thematrix H⁺ with the elements h, of the matrix H⁺ replaced by theestimates ĥ_(i,k) for i=−M₁, . . . , 0, . . . , M₁ and with the matrixH⁺ given by (83).

$\begin{matrix}{H^{+} = \begin{bmatrix}H_{1}^{+} \\H_{2}^{+} \\H_{3}^{+}\end{bmatrix}} & ( {83a} ) \\{{{H_{1}^{+} = \begin{bmatrix}h_{- M_{1}} & 0 & 0 & {{......}...} & 0 \\h_{{- M_{1}} + 1} & h_{- M_{1}} & 0 & \ldots & 0 \\\; & \ldots & \ldots & \ldots & \; \\h_{{- M_{1}} + N_{1}} & \ldots & \ldots & \ldots & h_{- M_{1}}\end{bmatrix}};}{H_{2}^{+} = \begin{bmatrix}h_{{- M_{1}} + N_{1} + 1} & 0 & 0 & \ldots & h_{{- M_{1}} + 1} \\\; & \ldots & \ldots & \ldots & \; \\h_{M_{1}} & \ldots & \ldots & \ldots & h_{M_{1} - N_{1}}\end{bmatrix}}} & ( {83b} ) \\{H_{3}^{+} = \begin{bmatrix}0 & h_{M_{1}} & 0 & {{......}...} & h_{M_{1} - N_{1} + 1} \\0 & 0 & h_{M_{1}} & {{......}...} & h_{M_{1} - N_{1} + 2} \\\; & \; & \; & {{......}...} & \; \\0 & 0 & {{......}...} & {{......}...} & h_{M_{1}}\end{bmatrix}} & ( {83c} )\end{matrix}$In (83b, c) 2M₁ is assumed to be greater than N₁. More generally thematrix H⁺ is obtained by N+M₁ shifted versions of the channel impulseresponse vector h, appended with appropriate number of Os on both sidesof h, staring with the first row equal to the first row of the matrix H₁⁺ in (83b). In (81)-(82) N₂ is selected equal to M₁. The secondcorrection signal vector w _(k) ^(c) ² in (80a) is obtained byminimizing the norm of the vector with ( ĝ _(k) ^(m)− δ) with respect tothe vectors ŵ _(k) ⁺ and ŵ _(k) ⁻. Equivalently the result is obtainedby minimizing the objective function J_(L) ₂ in (84a)J _(L) ₂ =(H _(k) ^(c) w− δ _(K) ₁ _(,N) ₂ )^(H)(H _(k) ^(c) w− δ _(K) ₁_(,N) ₂ )  (84a)with respect to the equalizer parameter vector w. In (84a) H_(k) ^(c) isthe matrix given by (84b).

$\begin{matrix}{H_{k}^{c} = \lbrack {H_{k}^{+}\underset{I_{M_{1}}}{{\vdots O}_{{({K_{1} + 1})} \times M_{1}}}} \rbrack} & ( {84b} )\end{matrix}$In (84b) O_((K) ₁ _(+1)×M) ₁ is the (K₁+1)×M₁ matrix with all theelements equal to 0 and I_(M) ₁ is the (M₁×M₁) identity matrix. Thesecond correction signal vector w _(k) ^(c) ² is given byŵ _(k) ^(c) ² =Ĥ _(k) ^(cH)(Ĥ _(k) ^(c) ŵ _(k)−{circumflex over (δ)}_(K)₁ _(,N) ₂ )*  (85)

With the application of (84b), the second correction signal vector w_(k) ^(c) ² may be written in the equivalent form in (86).

$\begin{matrix}{{\overset{\_}{w}}_{k}^{c_{2}} = {\begin{bmatrix}H_{k}^{+ H} \\{{{{{......}...}...}...}...} \\{O_{M_{1} \times {({K_{1} + 1})}}I_{M_{1}}}\end{bmatrix}( {{\hat{\overset{\_}{g}}}_{k}^{m} - {\overset{\_}{\delta}}_{K_{1},N_{2}}} )^{*}}} & ( {86a} ) \\{{\hat{\overset{\_}{g}}}_{k}^{m} = {{H_{k}^{+}{\hat{\overset{\_}{w}}}_{k}^{+}} + {\hat{\overset{\_}{w}}}_{k}^{- e}}} & ( {86b} )\end{matrix}$With ĝ _(k) ^(m) split as

$\begin{matrix}{{\hat{\overset{\_}{g}}}_{k}^{m} = \lbrack {( {\hat{\overset{\_}{g}}}_{k}^{1m} )^{T}( {\hat{\overset{\_}{g}}}_{k}^{2m} )^{T}} \rbrack^{T}} & ( {86c} ) \\{{\overset{\_}{w}}_{k}^{c_{2}} = \begin{bmatrix}{H_{k}^{+ T}( {{\hat{\overset{\_}{g}}}_{k}^{m} - {\overset{\_}{\delta}}_{K_{1},N_{2}}} )} \\{\hat{\overset{-}{g}}}_{k}^{2m}\end{bmatrix}^{*}} & ( {86d} )\end{matrix}$In (86c) ĝ _(k) ^(1m) and ĝ _(k) ^(2m) are vectors of dimension (K₁+1)and N₂ respectively.

FIG. 10 shows the block diagram of the BMAEHS block 60 of FIG. 1 for oneof the embodiments of the invention incorporating the case of thedecision feedback equalizer. Referring to FIG. 10, the normalizedchannel output 8 z_(k+K) ₁ is input to a cascade of N₁ delay elements801 providing the delayed versions 802 of z_(k+K) ₁ denoted by z_(k+K) ₁⁻¹, . . . , z_(k+K) ₁ _(−N) ₁ at their respective outputs. Thenormalized channel output 8 and its N₁ various delayed versions 802 areinput to the (N₁+1) wm multipliers 803 wm₁, . . . wm_(N) ₁ ₊₁. The N wmmultipliers 803, 815 are inputted by the conjugates of the components ofthe equalizer parameter vector ŵ_(−N) ₁ _(,k), . . . , ŵ_(0,k), . . . ,ŵ_(N) ₂ _(,k). provided by the conjugate blocks 804, 816 that areinputted with the components 805 of the equalizer parameter vector ŵ_(k). The (N₁+1) wm multipliers 803 multiply the normalized channeloutput and its N₁ delayed versions 802 by the conjugates 806 of thefirst N₁ components of the equalizer parameter vector ŵ _(k) generatingthe respective products 807 at the outputs of the wm multipliers 803.The outputs 807 of the (N₁+1) wm multipliers are input to the summer 808that provides a linear estimate 809 â_(k+M) ₁ of the data symbol at theoutput of the summer 808. The linear estimate 809 â_(k+M) ₁ is input tothe decision device 11 that generates the detected symbol 12 a_(k+M) ₁^(d) based on the decision function Δ( ) given by (20)-(25).

Referring to FIG. 10, the detected symbol 12 a_(k+M) ₁ ^(d) is input tothe cascade of N₂ delays 814 providing the N₂ delayed versions 812 ofa_(k+M) ₁ ^(d) denoted by a_(k+M) ₁ ⁻¹ ^(d), . . . , a_(k+M) ₁ _(−N) ₂^(d) at their respective outputs. The N₂ delayed versions 812 of a_(k+M)₁ ^(d) are input to the N₂ wm multipliers 815 wm_(N) ₁ ₊₂, . . . ,wm_(N) and are multiplied by complex conjugates 817 of the last N₂components 805 of the equalizer parameter vector ŵ_(1,k), . . . , ŵ_(N)₂ _(,k) in the N₂ wm multipliers 815 generating the respective products818 at the outputs of the N₂ wm multipliers. The outputs 818 of the N₂wm multipliers 815 are input to the summer 808 that provides the linearestimate 809 â_(k+M) ₁ of the data symbol at the output. The components802, 812 z_(k+K) ₁ , . . . , z_(k+K) ₁ _(−N) ₁ , a_(k+M) ₁ ⁻¹ ^(d), . .. , a_(k+M) ₁ _(−N) ₂ ^(d) of the state vector ψ _(k) are inputted tothe wcm multipliers 820 wcm₁, . . . , wcm_(N) that multiply thecomponents of ψ _(k) by μ_(d)e_(k)* with the outputs of the multipliersconstituting the components 830 of the vector μ_(d) ŵ _(k) ^(c) ¹ madeavailable to the N wca adders 832 wca₁, . . . , wca_(N). Referring toFIG. 10, the linear estimate 809 â_(k+M) ₁ and the detected symbol 12a_(k+M) ₁ ^(d) are inputted to the adder 823 that provides the errorsignal 824 e_(k)=(a_(k+M) ₁ ^(d)−â_(k+M) ₁ ) to the input of theconjugate block 825. The output 826 of the conjugate block 825 ismultiplied by the scalar μ_(d) in the multiplier 827 with the output 826inputted to the N wcm multipliers 820 wcm₁, . . . , wcm_(N).

Referring to FIG. 10, the detected symbol 12 a_(k+M) ₁ ^(d) is inputtedto the channel estimator 440. The normalized channel output 8 z_(k+K) ₁is input to the delay block 435 that introduces a delay of K₁ samplesproviding the delayed version 436 z_(k) to the input of the channelestimator 440. The channel estimator 440 provides the estimate of thechannel impulse response vector 442 ĥ _(k) at the output of the channelestimator. The equalizer parameters 805 ŵ_(−N) ₁ _(,k), . . . , ŵ_(0,k),. . . , ŵ_(N) ₂ _(,k) are input to the scalar to vector converter 840that provides the equalizer vector 841 ŵ _(k) to the correction signalgenerator for DFE block 850. The estimate of the channel impulseresponse vector 442 ĥ _(k) is input to the correction signal generatorfor DFE block 850 that provides the second correction signal vector 842w _(k) ^(c) ² to the multiplier 843. The correction signal generator forDFE 850 estimates the impulse response ĝ _(k) ^(mT) of the cascade ofthe channel and the equalizer. The difference between the vector ĝ _(k)^(mT) and the ideal impulse response vector

${{\overset{\_}{\delta}}_{K_{1},N_{2}}}^{T} = \lbrack {\underset{\underset{K_{1}}{︸}}{00\mspace{14mu}\ldots\mspace{14mu} 0}\mspace{20mu} 1\mspace{20mu}\underset{\underset{N_{2}}{︸}}{\mspace{11mu}{00\mspace{14mu}\ldots\mspace{14mu} 0}}} \rbrack$may provide a measure of the modeling error incurred by the equalizer. Alarge deviation of the convolved response ĝ _(k) ^(T) from the idealimpulse response implies a relatively large modeling error.

The correction signal generator block 850 generates the secondcorrection signal 842 w _(k) on the basis of the modeling error vector [δ _(K) ₁ _(,N) ₂ − ĝ _(k)] and is given by (85)-(86). The secondcorrection signal 842 w _(k) ^(c) ² is inputted to the adaptation block16B for adjusting the equalizer parameter vector ŵ _(k+1) at time k+1.The decision feedback equalizer parameter algorithm implemented by theadaptation block 16B of FIG. 10 is described by (80). Referring to FIG.10, the second correction signal 842 w _(k) ^(c) ² is multiplied by apositive scalar μ providing the product to the vector to serialconverter 845. The outputs ŵ_(−N) ₁ _(,k) ^(c) ² , . . . , ŵ_(N) ₂ _(,k)^(c) ² are inputted to the N wca adders 832. The outputs of the N wcaadders 832 constituting the components of the updated equalizerparameter vector ŵ _(k+l) are inputted to the N delays 834. The outputsof the N delays 834 are inputted to the N conjugate blocks 804.

FIG. 11 shows the block diagram of the correction signal generator forthe decision feedback equalizer 850 of FIG. 10. Referring to FIG. 11,the estimate of the channel impulse response vector 442 ĥ _(k) is inputto the matrix Ĥ_(k) ⁺ collator 860 that forms matrix 861 Ĥ_(k) ⁺according to equation (83a) with h_(i) in (83) replaced by ĥ_(i) fori=M₁, . . . 0 . . . , M₁. The equalizer parameter vector 841 ŵ _(k) isinput to the vector splitter 864 that provides two vectors 865 ŵ _(k)⁺=[ŵ_(−N) ₁ _(,k), . . . , ŵ_(0,k)]^(T) and 866 ŵ _(k)=[ŵ_(1,k), . . .ŵ_(N) ₂ _(,k)]^(T) defined in (81b) at the output where N₂ may be equalto M₁. Referring to FIG. 11, the matrix 861 Ĥ_(k) ⁺ and the vector 865 ŵ_(k) ⁺ are inputted to the matrix multiplier 867 that provides theproduct 868 ĝ _(k) ⁺=Ĥ_(k) ⁺ ŵ _(k) ⁺ at the matrix multiplier 867output. The vector 868 ĝ _(k) ⁺ is input to the vector to scalarconverter 870 that provides the components 871, 872, 875 ĝ_(−K) ₁ _(,k)⁺, . . . , ĝ_(0,k) ⁺, . . . , ĝ_(N) ₂ _(,k) ⁺ at the output of thevector to scalar converter 870. The first K₁ components 871 ĝ_(−K) ₁_(,k) ⁺, . . . , ĝ_(−1,k) ⁺ of the vector ĝ _(k) ⁺ (are input to thescalar to vector converter 880. The component 872 ĝ _(k) ⁺ subtracts theconstant 1 in the adder 873 with the result of the subtraction 874 ( ĝ_(0,k) ⁺−1) inputted to the scalar to vector converter 880 as shown inFIG. 11. The scalar to vector converter 880 provides the vector 883 ( ĝ_(k) ^(1m)− δ _(K) ₁ _(,0)) at the output where ĝ _(k) ^(1m)=[ĝ_(−K) ₁_(,k), . . . , ĝ_(0,k) ⁺]^(T) and δ _(K) ₁ _(,0) is the discrete impulsevector with K₁ zeros followed by 1 as its components.

Referring to FIG. 11, the vector 841 ŵ _(k) ⁻ is inputted to the vectorto scalar converter 2 that provides the components 877 ŵ_(1,k), . . . ,ŵ_(N) ₂ _(,k) at the output of the vector to scalar converter 895. Thecomponents 877 ŵ_(1,k), . . . , ŵ_(N) ₂ _(,k) and the components 875ĝ_(1,k) ⁺, . . . ĝ_(N) ₂ _(,k) ⁺ of the vector ĝ _(k) ⁺ are inputted tothe adders 876 ga₁, . . . , ga_(N2). The N₂ ga_(i) adder 876, i=1, 2, .. . , N₂ provides the sum 879 (ĝ_(i,k) ⁺+ŵ_(i,k)) at the adder output.The outputs 879 of the N₂ ga adders 876 are input to the scalar tovector converter 882 that provides the vector 884 ĝ _(k) ^(2m) at theoutput. Referring to FIG. 11, the vectors ( ĝ _(k) ^(1m)−δ_(K) ₁ _(,0))and ĝ _(k) ^(2m) are inputted to the vector concatenator 885 thatconcatenates the input vectors in to the vector 888 ( ĝ _(k) ^(m)− δ_(K) ₁ _(,N) ₂ )=[( ĝ _(k) ^(1m)−δ_(K) ₁ _(,0))^(T)( ĝ _(k)^(2m))^(T)]^(T) of size (K₁+N₂+1) at the output of the vectorconcatenator 885 and provides the result to the matrix multiplier 886.The matrix 861 Ĥ_(k) ⁺ from the matrix Ĥ_(k) ⁺ collator block is inputto the transpose block 862 that provides the matrix 863 Ĥ_(k) ⁺ to theinput of the matrix multiplier 886. The matrix multiplier 886 providesthe product 887 Ĥ_(k) ^(+T)( ĝ _(k) ^(m)− δ _(K) ₁ _(,N) ₂ ) at thematrix multiplier 886 output and makes the result available to thevector concatenator 2. The vector ĝ _(k) ^(m) is inputted to the vectorconcatenator 2 that concatenates it with the vector Ĥ_(k) ^(+T)( ĝ _(k)^(m)− δ _(K) ₁ _(,N) ₂ ) providing the concatenated vector 891 to theconjugate block 892. The output 842 of the conjugate block 892 is equalto the second correction signal w _(k) ^(c) ² according to (86).

The convergence rate of the equalizer parameter vector update algorithmin (27) to (31) may be significantly increased by the application of theorthogonalization procedure In the orthogonalization procedure, thesequence of the correction signal vectors is modified such that in themodified sequence, the correction signal vectors at successive timeinstances k are nearly orthogonal resulting in increased convergencerate. In one of the various embodiments of the invention, the BMAEHSblock of FIG. 1 is modified by an orthogonalizer.

FIG. 12 shows the block diagram of the BMAEHS block 70 incorporating thecorrection signal vector orthogonalizer that may replace the BMAEHSblock 60 in FIG. 1. Referring to FIG. 12, the normalized channel output8 z_(k+K) ₁ is input to the equalizer block 9(800), the number in theparenthesis refers to the case of the embodiment of the invention withthe decision feedback equalizer. The linear estimate â_(k+M) ₁ at theoutput of the equalizer filter is input to the decision device 11 thatgenerates the detected symbol 902 a_(k+M) ₁ ^(d) based on the decisionfunction Δ( ). The linear estimate 901 â_(k+M) ₁ is subtracted from thedetected symbol 902 a_(k+M) ₁ ^(d) by the adder 903 providing the errorsignal 904 e_(k)=(a_(k+M) ₁ ^(d)−â_(k+M) ₁ ). The complex conjugate ofthe error signal 904 e_(k) made available by the conjugate block 905 andthe equalizer state vector 907 ψ _(k) provided by the equalizer 9(800)are inputted to the matrix multiplier 910. The matrix multiplier 901generates the first correction signal vector 911 w _(k) ^(c) ¹ that thatis made available to the correction signal vectors normalizer 915.Referring to FIG. 12, the MEECGS block 50(810) provides the secondcorrection signal vector 912 w _(k) ^(c) ² to the correction signalvectors normalizer 915. The correction signal vectors normalize 915normalizes the two correction signal vectors 911, 912 by the squareroots of the mean squared norms of the respective correction signalvectors and inputs the normalized correction signal vectors 916 χ _(k) ¹and 917 χ _(k) ² to the adder 918. The adder 918 subtracts the vector χ_(k) ² from χ _(k) ¹ providing the difference 920 χ _(k)=μ₁ χ _(k) ¹−μ₂χ _(k) ² to the input of the orthogonalizer block 955. In variousalternative embodiments of the invention, the difference 920 χ _(k)= χ_(k) ¹− χ _(k) ² may be replaced by a weighted difference χ _(k)=μ₁ χ_(k) ¹−μ₂ χ _(k) ² for some positive weighting coefficients μ₁ and μ₂.

Referring to FIG. 12, the orthogonalizer 955 provides the orthogonalizedcorrection signal vector 955 K_(k) ^(e) at the output of theorthogonalizer evaluated according to equation (87a, b),)K _(k) ^(e) =Q _(k) χ _(k) =Q _(k−1) χ _(k)( χ _(k) ^(H) Q _(k−1) χ_(k)+λ_(J))⁻¹  (87a)Q _(k)=λ_(J) ⁻¹ [Q _(k−1) −Q _(k−1) χ _(k)( χ _(k) ^(H) Q _(k−1) χ_(k)+λ_(J))⁻¹ χ _(k) ^(H) Q _(k−1) ];k=0,1, . . .   (87b)

In (87b) the matrix Q⁻¹ may be set equal to εI_(N) with E equal to somepositive scalar and I_(N) denting the N×N identity matrix. In (87b)λ_(J) is an exponential data weighting coefficient with 0<λ_(J)≦1 anddetermines the rate at which the past values of 920 χ _(k) are discardedin the estimation of the matrix Q_(k) as with the application of thematrix inversion lemma, the matrix Q_(k) ⁻¹ for relatively large valueof k may be interpreted as a positive scalar times an estimate of thecovariance of χ _(k), with Q_(k) ⁻¹≅((1−λ_(J) ^(k))/(1−λ_(J)))E[ χ _(k)χ _(k) ^(H)] where E denotes the expected value operator.

Referring to FIG. 12, the normalized correction signal vector 920 χ _(k)is input to the matrix multiplier 921 wherein 920 χ _(k) is premultiplied by the matrix 922 Q_(k−1). The matrix 922 Q_(k−1) is madeavailable to the matrix multiplier 921 by the output of the delay 944.The output of the matrix multiplier 921 is input to the matrixmultiplier 926. The normalized correction signal vector 920 χ _(k) isinput to the conjugate transpose block 924 that provides the row vector929 χ _(k) ^(H) to the input of the matrix multiplier 926. The matrixmultiplier 921 output 923 equal to Q_(k−1) χ _(k) is inputted to thematrix multiplier 934 and to the conjugate transpose block 937. Thematrix multiplier 926 output 927 equal to χ _(k) ^(H)Q_(k−1) χ _(k) isinput to the adder 928 that adds the constant λ_(J) to the input 927.The output 931 of the adder 928 equal to ( χ _(k) ^(H)Q_(k−1) χ_(k)+λ_(J)) is input to the inverter 932 that makes the result 933 equalto 1/( χ _(k) ^(H)Q_(k−1) χ _(k)+λ_(J)) available to the input of thematrix multiplier 934. The matrix multiplier 934 output 935 equal toK_(k) ^(e)=Q_(k−1) χ _(k)/( χ _(k) ^(H)Q_(k−1) χ _(k)+λ_(J))=Q_(k) χ_(k) constitutes the orthogonalized correction signal vector K_(k) ^(e).The output 935 of the matrix multiplier 934 and the output of transposeblock 937 equal to χ _(k) ^(H)Q_(k−1) are inputted to the matrixmultiplier 936 that provides the matrix product 939 Q_(k−1) χ _(k) χ_(k) ^(H)Q_(k−1)/( χ _(k) ^(H)Q_(k−1) χ _(k)+λ_(J)) at the output of thematrix multiplier 936. The outputs of the delay 944 and that of thematrix multiplier 936 are input to the adder 940 that provides thedifference between the two inputs at the output of the adder. The output941 of the adder 940 is normalized by the constant λ_(J) in themultiplier 941. The output 943 of the multiplier 941 constitutes theupdated matrix 943 Q_(k) that is input to the delay 944. The output ofthe delay 944 equal to 922 Q_(k−1) is input to the multiplier 921.

Referring to FIG. 12, the normalized channel output 8 z_(k+K) ₁ is inputto the delay block 435 that introduces a delay of K₁ samples providingthe delayed version 436 z_(k) to the input of the channel estimator 440.The detected symbol 902 a_(k+M) ₁ _(d) from the output of the decisiondevice 11 is made available to the channel estimator 440. The channelestimator 440 provides the estimate of the channel impulse responsevector 442 ĥ _(k) at the output of the channel estimator and to theinput of the correction signal generator 450(850). In one of the variousembodiments of the invention the equalizer filter 9(800) in FIG. 12 isthe linear equalizer filter and the correction signal generator block isthe same as the correction signal generator block for LEQ 450 of FIG. 6for the BMAEHS with the linear equalizer. The correction signalgenerator 450 convolves the estimate of the channel impulse responsevector 442 ĥ _(k) with the equalizer parameter vector 950 ŵ _(k) ^(T) toobtain the convolved vector ĝ _(k) ^(T). The difference between thevector ĝ _(k) ^(T) obtained by convolving the estimate of the channelimpulse response vector with the equalizer parameter vector ŵ _(k), andthe ideal impulse response vector δ _(K) ₁ _(,K) ₂ ^(T) may provide ameasure of the modeling error incurred by the equalizer. A largedeviation of the convolved response ĝ _(k) ^(T) from the ideal impulseresponse implies a relatively large modeling error. The correctionsignal generator block 450 generates the second correction signal vector912 w _(k) ^(c) ² on the basis of the modeling error vector [ δ _(K) ₁_(,K) ₂ − ĝ _(k)]. The second correction signal vector 912 w _(k) ^(c) ²is inputted to the correction signal vectors normalizer block 915.

In an alternative embodiment of the invention, the equalizer filter9(800) in FIG. 12 is the decision feedback equalizer filter 800 and thecorrection signal generator block 450(850) is the same as the correctionsignal generator block DFE 850 of FIG. 10 for the BMAEHS with thedecision feedback equalizer. The correction signal generator block 850evaluates the second correction signal vector 912 w _(k) ^(c) ² andmakes it available to the correction signal vectors normalize 915.

Referring to FIG. 12, the orthogonalized correction signal vector 935K_(k) ^(e) available at the output of the orthogonalizer 955 is inputtedto the multiplier 945 that multiplies the vector 935 K_(k) ^(e) by apositive scalar μ. The scalar μ may be selected to be either a constantor may be a function of k. For example, μ may be equal to μ=μ₀(1−λ_(J)^(k))/(1−λ_(J)) for some positive scalar μ₀ and with 0<λ_(J)<1. Such atime-varying μ normalizes the matrix 943 Q_(k) in (87a) effectivelyreplacing Q_(k) ⁻¹ by ((1−λ_(J))/(1−λ_(J) ^(k)))Q_(k) ⁻¹≅E[ χ _(k) χ_(k) ^(T)]. Referring to FIG. 12, the output 946 of the multiplier 945equal to μK_(k) ^(e) is inputted to the adder 947 that adds the input947 μK_(k) ^(e) to the other input 950 of the adder equal to ŵ _(k) madeavailable from the output of the delay 949. The output 948 of the adder947 constitutes the updated equalizer parameter vector given ŵ _(k+1) byŵ _(k+1) = ŵ _(k) +μK _(k) ^(e)  (88)The vector 948 ŵ _(k+1) is input to the delay 949 providing the delayedversion of the input ŵ _(k) at the output of the delay. Referring toFIG. 12, the equalizer parameter vector 950 ŵ _(k) is input to thecorrection signal generator 450(850) and the vector to scale converter991. The vector to scalar converter 991 provides the components 992ŵ_(−N) ₁ _(,k) ^(c) ² , . . . , ŵ_(0,k) ^(c) ² , . . . , ŵ_(N) ₂ _(,k)^(c) ² with N₂ possibly equal to N₁, of the equalizer parameter vector950 ŵ_(k) to the equalizer block that provides the linear estimate ofthe data symbol 901 â_(k+M) ₁ at the equalizer filter output.

FIG. 13 shows the correction signal vectors normalizer 915. Referring toFIG. 13, the first correction signal vector 911 w ^(c) ¹ is input to thenorm square block 951 that provides the output 953 p_(k)=∥ w ^(c) ¹ ∥².The signal 953 p_(k) is input to the accumulator 952 Acc1 thataccumulates the input 953 p_(k) according to the equationp _(k) ^(a)=λ_(c) p _(k−1) ^(a) +p _(k) ;p ⁻¹ ^(a) =c ₁ ;p _(k) =∥ w_(k) ^(c) ¹ ∥² ;k=0,1, . . .   (89a)where λ_(c) with 0<λ_(c)≦1 is the exponential data weightingcoefficient. The accumulator Acc1 952 is comprised of an adder 954, adelay 956, and a multiplier 958. The delay 956 is inputted with theaccumulator output 955 p_(k) ^(a) and provides the delayed version 957p_(k−1) ^(a) to the input of the multiplier 958 that multiplies theinput 957 by λ_(p) and provides the product 959 to the adder 954. Theadder 954 sums the input 953 p_(k) and the multiplier output 959λ_(c)p_(k−1) ^(a) providing the sum 955 p_(k) ^(a) at the output of theadder. Referring to FIG. 13, the constant 1 is input to the accumulatorAcc2 962 that results in the output of the accumulator Acc2 962 given byequation (89b)κ_(k)=λ_(c)κ_(k−1)+1;κ_(k)=(1−λ_(c))/(1−λ_(c) ^(k))  (89b)The outputs of the accumulators Acc1 960 and Acc2 962 are input to thedivider 961 that makes the result of the division 966 p_(k) ^(f)=p_(k)^(a)/κ_(k) available at the output of the divider. The signal 966 p_(k)^(f) is input the square root block 967 that makes the result 968√{square root over (p_(k) ^(f))} available to the divider 970. The firstcorrection signal vector 911 w ^(c) ¹ is input to the divider 970 and isdivided by the other input of the divider equal to 968 √{square rootover (p_(k) ^(f))} and makes the normalized correction signal 1 vector916 χ _(k) ¹= w _(k) ^(c) ¹ /√{square root over (p_(k) ^(f))} availableat the output of the divider 970.

Referring to FIG. 13, the second correction signal vector 912 w _(k)^(c) ² is input the mean square 2 estimator 980 that is comprised of thenorm square block 971, the adder 974, the delay 976, the multiplier 978,and the divider 981. The operation of the mean square 2 estimator 980 issimilar to that of the mean square 1 estimator 960 and provides theresult 982 q_(k) ^(f) evaluated according to (89c, d) to the square rootblock 983 that provides the output 984 √{square root over (q_(k) ^(f))}to the divider 985. The second correction signal vector 912 w ^(c) ² isinput to the divider 985 that normalized the second correction signalvector 912 w _(k) ^(c) ² providing the second normalized correctionsignal vector 917 χ _(k) ²= w _(k) ^(c) ² /√{square root over (q_(k)^(f))} at the output of the divider 985.q _(k) ^(a)=λ_(c) q _(k−1) ^(a) +q _(k) ;q ⁻¹ ^(a) =c ₂ ;q _(k) =∥ w_(k) ^(c) ² ∥² ;k=0,1, . . .   (89c)p _(k) ^(f) =p _(k) ^(a)(1−λ_(c))/(1−λ_(c) ^(k));q _(k) ^(f) =q _(k)^(a)(1−λ_(c))/(1−λ_(c) ^(k))  (89d)

Referring to FIGS. 6 and 10, in various embodiments of the invention,positive scalars μ_(d) and μ therein may alternatively be selectedaccording toμ_(d)=μ₀/√{square root over (p _(k) ^(f))};μ=μ₀/√{square root over (q_(k) ^(f))}  (90)with p_(k) ^(f) and q_(k) ^(f) evaluated according to (89). In (90) μ₀is some positive scalar.

The equalizer total error variance equal to E[|a_(k)−a_(k) ^(d)|²] withE denoting the expected value operator is in general dependent upon thesize N of the equalizer parameter vector. Increasing N may result in thereduction of the equalizer total error variance, however it requires ahigher computational complexity. For the BMAEHS of the invention, thedominant term in the number of computations per iteration of theequalizer parameter update algorithm is proportional to N². Thusdoubling the size N of the equalizer parameter vector, for example,results in an increase in the number of computations by factor of four.The BMAEHS reduces the equalizer total error variance to a relativelysmall value even for a relatively small value of N, for example with Nin the range of 10-20.

The equalizer total error variance can be further reduced while keepingthe total number of computations required per iteration to a minimum byadding a second equalizer in cascade with the BMAEHS. The equalizertotal error variance E[|a_(k)−a_(k) ^(d)|²] achieved by the BMAEHS afterthe initial convergence period is relatively small implying theconvolution g _(k) of the channel impulse response vector h with theequalizer parameter vector ŵ _(k) is close to the discrete impulsevector δ=[0 . . . 010 . . . 0]^(T). The linear estimate â_(k) of thedata symbol may be considered to be the output of an unknown equivalentchannel with impulse response vector g _(k) with the input to theequivalent channel equal to a_(k).

FIG. 14 shows the block diagram of the cascaded equalizer 90. The blindmode adaptive equalizer equalizer (BMAE) 2 1060 in the cascadedequalizer of FIG. 14 estimates the data a_(k) on the basis of the input²z_(k) to the equalizer 2 made equal to the linear estimate a_(k)provided by the BMAEHS with equalizer 2 1060 parameter vector of lengthN′=N′₁+N′₂+1. During the initial stage of the convergence of equalizer 21060, the symbol a_(k) required in the adaptation algorithm for theequalizer 2 1060 is replaced by the detected data symbol a_(k) ^(d)provided by the BMAEHS. After the initial convergence period of theequalizer 2, the symbol a_(k) required in the adaptation algorithm forthe equalizer 2 is replaced by the detected data symbol ²a_(k) ^(d) atthe output of equalizer 2. The detected data ²a_(k) ^(d) at the outputof the equalizer 2 is expected to be more accurate than a_(k) ^(d). Theperformance of the cascaded equalizer may be considered to be equivalentto that of the single BMAEHS equalizer with equalizer parameter vectorsize N+N′ but with significantly much smaller computationalrequirements. In view of the impulse response vector g _(k) of theequivalent channel being close to the discrete impulse vector δ, theadaptation algorithm for the equalizer 2 may, for example, be selectedto be the LMS, RLS or QS algorithm without the need for hierarchicalstructure of the algorithm. In some embodiments of the invention, thestage 2 equalizer may also be a BMAEHS operating on the unknown channelwith impulse response vector g _(k).

Referring to FIG. 14, the normalized channel output 8 z_(k+K) ₁ is inputto the BMAEHS block 60 that provides the detected symbol 12 a_(k+M) ₁^(d) at the output. Referring to FIG. 14, the detected data symbol 12a_(k+M) ₁ ^(d) and the linear estimate of the data symbol 10 â_(k+M) ₁that is equal to 1008 ²z_(k+K) ₁ , are inputted to the blind modeadaptive equalizer 2 1060. Referring to FIG. 14, the linear estimate ofthe data symbol 10 â_(k+M) ₁ is input to the equalizer filter 2 1009with the equalizer parameter vector ŵ _(k) ²=[ŵ_(−N′) ₁ ², . . . , ŵ₀ ²,. . . ŵ_(N′) ₂ ²]^(T) and with the length of the equalizer 2 1009 equalto N′=N′₁+N′₂+1. In one of the various embodiments of the invention, theequalizer 2 1009 in the blind mode adaptive equalizer 2 block 1060 is alinear equalizer with N′₁=N′₂ with its block diagram same as that givenin FIG. 6. In various other embodiments of the invention, the equalizer2 1009 may be a decision feedback equalizer. The equalizer 2 1009 isinitialized with the initial parameter vector estimate ŵ ₀ ²=δ_(N′) ₁_(,N′) ₂ =[0 . . . 010 . . . 0]^(T). The state vector 1014 of equalizer2 1009 given by ² ψ _(k)=[²z_(k+M) ₁ , . . . , ²z_(k+M) ₁ _(−N′) ₁ , . .. , ²z_(k+M) ₁ _(−N′+1)]^(T) is input to the adaptation block 2 1016 ofthe blind mode adaptive equalizer 2 1060.

Referring to FIG. 14, the block diagram of the adaptation block 2 1016of the blind mode adaptive equalizer 2 1060 is similar to that ofadaptation block 16 given by FIG. 6 with the second correction signalvector w ^(c) ² in the figure possibly set to 0. The parameter updateequation for the adaptation block 2 1016 is given byŵ _(k+1) ² = ŵ _(k) ²+μ₂ ² ψ _(k)(a _(k+M) ₁ _(N′) ₁ −² a _(k+M) ₁_(−N′) ₁ )*;k=0,1, . . . ;  (91a)ŵ ₀ ²= δ _(N′) ₁ _(,N′) ₂ =[0 . . . 010 . . . 0]^(T)  (92b)

The iteration in (91a) is performed by the adaptation block 1016 fork≧0. However, the equalizer 2 1009 parameter vector in the blind modeadaptive equalizer 2 is frozen at the initial condition ŵ ₀ ² during thefirst N′_(d) iterations of (91a) and is updated after the initial N′_(d)iteration of (91a) by the output 1033 of switch S3 by closing the switchS₃ 1023 after the initial N′_(d) iteration of (91a), atk+M₁=N_(d)+N′₁+N′_(d) where N_(d) and N′_(d) are the convergence periodsof the BMAEHS 60 and the blind mode adaptive equalizer 2 1060respectively. The convergence period N_(d) is the time taken by theequalizer in the BMAEHS 60 to achieve some relatively small mean squareerror after the first N₁ samples of the normalized channel output isinputted into the equalizer and may be selected to be about 100-200samples. The convergence period N′_(d) of the blind mode adaptiveequalizer 2 1060 is similarly defined.

Referring to FIG. 14, the linear estimate 1010 of the data symbolâ_(k+M) ₁ _(−N′) _(i) is input to the decision device 1011 that providesthe second detected data symbol 1012 ² a_(k+M) ₁ _(−N′) ₁ ^(d) at theoutput of the device according to the decision function D( ) that may begiven by (20)-(25). The detected data symbol 1012 ² a_(k+M) ₁ _(−N′) ₁is connected to the input 2 of the switch S₄ 1026. The detected datasymbol 12 a_(k+M) ₁ ^(d) from the BMAEHS 60 is inputted to the delay1013 that provides a delayed version 1018 of the detected data symbola_(k+M) ₁ _(N′) ₁ ^(d) to the position 1 of the switch S₄ 1026. Theoutput 1040 of the switch S₄ 1026 is connected to the position 1 of theswitch S₄ 1026 for k+M₁<N_(d)+N′₁+N′_(d) and is in position 2 fork+M₁≧N_(d)+N′₁+N′_(d). The output 1040 a_(k+M) ₁ _(−N′) ₁ ^(c) of theswitch S₄ 1026 is the final detected output of the cascaded equalizer.The final detected symbol 1040 of the cascaded equalizer is equal to thedelayed version 1018 of the detected symbol a_(k+M) ₁ _(−N′) ₁ ^(d) fromthe BMAEHS 60 for k+M₁<N_(d)+N′₁+N′_(d) and is equal to the seconddetected data symbol 1012 ² a_(k+M) ₁ _(−N′) ₁ ^(d) fork+M₁≧N_(d)+N′₁+N′_(d) and is based on the combined equalization fromboth the stage 1 BMAEHS 60 and the stage 2 blind mode adaptive equalizer2 1060 of the cascaded equalizer. Referring to FIG. 14, the finaldetected symbol 1040 is inputted to the adaptation block 2 1016 and tothe delay 1030. The output 1032 of the delay is inputted to theequalizer filter 2 1009.

One of the various embodiments of the invention relates to the problemof adaptive beam former for recovering data symbol transmitted form asource in a blind mode. FIG. 15 shows the embodiment of the inventionfor the problem of adaptive digital beam former. As shown in the Figure,a source transmitter 1210 inputs an RF signal obtained by the basebandto RF conversion, not shown, of the source data symbols a_(k) to thetransmit antenna 1215 for transmission. The transmitted RF signal isreceived by an array of N antennas 1202 a . . . n. The outputs 1222 ofthe antennas 1220 v_(R,1)(t), . . . , v_(R,N)(t) are input to the N RFfront end blocks 1225, a, . . . , n. The outputs 1226 of the N front endblocks V_(RF,1) (t), . . . , v_(RF,N)(t) are inputted to the respectiveN RF to baseband complex converters 1230 a, . . . , n. The complexbaseband signals 1232 v_(1,k), . . . , v_(N,k) are inputted to theadaptive digital beam former 1270 that provides the detected source datasymbols a_(k) ^(d) at the output. Referring to FIG. 15, the complexbaseband signals 1232 v_(1,k), . . . , v_(N,k) are inputted to the Nmultipliers 1235 a . . . n. The N multipliers 1235 a . . . n multiplythe inputs by the respective weights ŵ_(1,k) ^(m), . . . , ŵ_(N,k) ^(m)made available by the multilevel adaptation block 1280. The outputs 1236of the multipliers z_(1,k), . . . , z_(N,k) are summed by the adder 1238providing the signal 1239 s_(k) at the output. The adder output 1239s_(k) is inputted to the combiner gain normalizer block 1250 providingthe linear estimate of the data symbol 1252 â_(k) to the decisiondevice. The block diagram of the combiner gain normalizer block 1250 issimilar to that of the channel gain normalizer 7 of FIG. 1, except thatthe input z_(k) to the block 7 is replaced by the input 1239 s_(k). Thedecision device is similar to that given by the block 11 of FIG. 1.

Referring to FIG. 15, the multilevel adaptation block 1280 generates thefirst correction signal vector w_(k) ^(c) ¹ to minimize the errorbetween â_(k) and a_(k) ^(d) by minimizing the function

$\begin{matrix}{I_{1} = {E\lbrack {{a_{k}^{d} - {\hat{a}}_{k}}}^{2} \rbrack}} & (92) \\{{\hat{a}}_{k} = {{s_{k}/G_{k}^{m}} = {\frac{1}{G_{k}^{m}}{\hat{\overset{\_}{w}}}_{k}^{bT}{\overset{\_}{v}}_{k}}}} & (93)\end{matrix}$where G_(k) ^(m) is the modified gain estimate obtained by the combinergain normalizer 1250, v _(k)=[v_(1,k), v_(2,k), . . . , v_(N,k)]^(T) andŵ _(k) ^(b)=[ŵ_(1,k) ^(b), . . . , ŵ_(N,k) ^(b)]^(T) is the beam formerweight vector. Substitution of â_(k) form (93) in (92) results inI ₁ =E[|a _(k) ^(d) − ŵ _(k) ^(T) v _(k)|²]  (94)where ŵ _(k)= ŵ _(k) ^(b)/G_(k) ^(m) is the normalized beam formerweight vector. The gradient of I₁ with respect to ŵ _(k) is given by

$\begin{matrix}{\frac{\partial I_{1}}{\partial{\hat{\overset{\_}{w}}}_{k}} = {- {E\lbrack {{\overset{\_}{v}}_{k}( {a_{k}^{d} - {{\hat{\overset{\_}{w}}}_{k}^{T}{\overset{\_}{v}}_{k}}} )}^{*} \rbrack}}} & (95)\end{matrix}$From (95) the first correction signal vector w_(k) ^(c) ¹ is given byw _(k) ^(c) ¹ = v _(k)(a _(k) ^(d) − ŵ _(k) ^(T) v _(k))*  (96)

The second correction signal vector w_(k) ^(c) ² is derived on the basisof the model error. Referring to FIG. 15, the complex baseband signalvector v _(k) is given byv _(k) =a _(k) g+ n _(k)  (97)In (97) g _(k)=[g_(1,k), g_(2,k), . . . , g_(N,k)]^(T) is a scalar gaintimes the antenna array direction vector and n _(k) is the noise vector.From (93) and (97) one obtainsâ _(k) = ŵ _(k) ^(T) ga _(k) + ŵ _(k) ^(T) n _(k)  (98)Thus ignoring the noise term in (8) the linear estimate of the datasymbol â_(k) will be equal to a_(k) if w _(k) ^(T) g=1 and thedifference is the model error. Thus the model error is minimized by theminimization of the functionI ₂ =E[|1− ŵ _(k) ^(T) g| ²]  (99)The gradient of I₂ with respect to ŵ _(k) is given by

$\begin{matrix}{\frac{\partial I_{2}}{\partial{\hat{\overset{\_}{w}}}_{k}} = {- {E\lbrack {\overset{\_}{g}( {1 - {{\overset{\_}{w}}_{k}^{T}\overset{\_}{g}}} )}^{*} \rbrack}}} & (100)\end{matrix}$Replacing a_(k) by a_(k) ^(d) in (97) results in the followingexponentially data weighted Kaman filter algorithm for the estimate ofg,ĝ _(k) = ĝ _(k−1) +K _(k)( v _(k) −a _(k) ^(d) ĝ _(k−1))*;k=1,2, . . .  (101a)K _(k) =P _(k−1) a _(k)(|a _(k)|² P _(k−1) +λR _(k))⁻¹ =P _(k) a _(k) R_(k) ⁻¹  (101b)P _(k)=λ⁻¹ [P _(k−1) −|a _(k)|² P _(k−1)(|a _(k)|² P _(k−1) +λR _(k))⁻¹P _(k−1)]  (101c)

In (101) ĝ ₀ may be selected to be some a-priori estimate of g and P₀set equal to εI for some scalar ε>0 with I denoting the N×N identitymatrix. In (101) K_(k) is the Kaman gain matrix, P_(k) is the filtererror covariance matrix, R_(k) denotes the covariance matrix of thenoise vector n _(k) appearing in (97), and λ is the exponential dataweighting coefficient with 0<λ<1. In general R_(k) is an (N×N) matrixwith possibly nonzero off diagonal elements when the noise n _(k) isspatially correlated.

For the special case of uncorrelated spatial noise, R_(k) is a diagonalmatrix with R_(k)=r_(k) I and with r_(k) denoting the variance of eachcomponent of n _(k). With the matrix P₀ selected to be a diagonalmatrix, and R_(k) a diagonal matrix, P_(k) from (101c) is also diagonalfor all k>0. With P_(k) diagonal with P_(k)=p_(k)I for some scalarp_(k)>0, equation (101c) may be simplified to

$\begin{matrix}{{p_{k} = {\frac{r_{k}}{{\lambda\; r_{k}} + {a_{k}}^{2}}p_{k - 1}}};{k > 0}} & ( {101d} )\end{matrix}$Replacing g by its estimate ĝ _(k) in (100) results in the secondcorrection signal vector given byw _(k) ^(c) ² = ĝ _(k)(1− ŵ _(k) ^(T) ĝ _(k))*  (102)

The robustness of the adaptive beam former may be further increased bysimultaneously maximizing the signal to noise power ratio at thecombiner output by maximizing the signal power at the output of thecombiner while keeping the norm of the combiner weight vector ŵ _(k)close to 1. Equivalently the objective function I₃ given by (103) isminimized with respect to ŵ _(k).I ₃=½κ(1−∥ ŵ _(k)∥²)² −E[| ŵ ^(T) v _(k)|²]  (103)In (103) κ is some positive weighting scalar. The gradient of I₃ in(103) with respect to ŵ _(k) is given by∂I ₃ /∂ ŵ _(k)=κ(1−∥ ŵ _(k)∥²) ŵ* _(k) −E[ v _(k) â*]  (104)

From (104), a third correction signal vector is given byŵ _(k) ^(c) ³ = v _(k) â*−κ(1−∥ ŵ _(k)∥²) ŵ _(k)*  (105)The update algorithm implemented by the multilevel adaptation block 1280is given byŵ _(k+1) = ŵ _(k)+μ₁ v _(k)(a _(k) ^(d) − ŵ _(k) ^(T) v _(k))*+μ₂ ĝ_(k)(1− ŵ _(k) ^(T) ĝ _(k))*+μ₃ v _(k) â*−μ ₄(1−∥ ŵ _(k)∥²) ŵ_(k)*  (106a)ŵ _(k+1) ^(b) = ŵ _(k+1) /G _(k) ^(m) ;k=0,1, . . .   (106b)with the combiner gain G_(k) ^(m) inputted by block 1250, ĝ _(k) updatedaccording to (101) and μ₁, μ₂, μ₃ and μ₄ equal to some small positivescalars to achieve convergence of (106). The initial estimate ŵ ₀ in(106a) may be some a priori estimate of w.

Various modifications and other embodiments of the invention applicableto various problems in Engineering and other fields will be readilyapparent to those skilled in the art in the field of invention. Forexample, the architecture of the beam former can also be applied to theproblem of diversity combining. In various other possible modifications,the level 1 adaptive system of FIG. 1 can be modified to include theconstant modulus algorithm in those cases where the data symbol haveconstant modulus to provide additional robustness to the CMA basedequalizers. As another example, the adaptive digital beam formerarchitecture can be generalized to the case of broadband source whereinthe various antenna gains and combiner weights are replaced by digitalfilters similar to the equalizer filter 9 of FIG. 1. The equalizerarchitectures of the invention can be readily modified and applied tovarious fields where an equalizer or combiner architecture is applicablebut without the requirements of any training sequences. Examples of suchfields include radio astronomy, seismology, digital audio signalprocessing and so on.

It is to be understood that the figures and descriptions of the presentinvention have been simplified to illustrate elements that are relevantfor a clear understanding of the present invention, while eliminatingother elements, for purposes of clarity. Those of ordinary skill in theart will recognize that these and other elements may be desirable.However, because such elements are well known in the art and becausethey do not facilitate a better understanding of the present invention,a discussion of such elements is not provided herein.

In general, it will be apparent to one of ordinary skill in the art thatat least some of the embodiments described herein, including, forexample, all of the modules of FIG. 1, may be implemented in manydifferent embodiments of software, firmware, and/or hardware, forexample, based on Field Programmable Gate Array (FPGA) chips orimplemented in Application Specific Integrated Circuits (ASICS). Thesoftware and firmware code may be executed by a computer or computingdevice comprising a processor (e.g., a DSP or any other similarprocessing circuit) including, for example, the computing device 1600described below. The processor may be in communication with memory oranother computer readable medium comprising the software code. Thesoftware code or specialized control hardware that may be used toimplement embodiments is not limiting. For example, embodimentsdescribed herein may be implemented in computer software using anysuitable computer software language type, using, for example,conventional or object-oriented techniques. Such software may be storedon any type of suitable computer-readable medium or media, such as, forexample, a magnetic or optical storage medium. According to variousembodiments, the software may be firmware stored at an EEPROM and/orother non-volatile memory associated a DSP or other similar processingcircuit. The operation and behavior of the embodiments may be describedwithout specific reference to specific software code or specializedhardware components. The absence of such specific references isfeasible, because it is clearly understood that artisans of ordinaryskill would be able to design software and control hardware to implementthe embodiments based on the present description with no more thanreasonable effort and without undue experimentation.

FIG. 16 shows an example of a computing device 1600 according to oneembodiment. For the sake of clarity, the computing device 1600 isillustrated and described here in the context of a single computingdevice. However, it is to be appreciated and understood that any numberof suitably configured computing devices can be used to implement adescribed embodiment. For example, in at least some implementations,multiple communicatively linked computing devices may be used. One ormore of these devices can be communicatively linked in any suitable waysuch as via one or more networks. One or more networks can include,without limitation: the Internet, one or more local area networks(LANs), one or more wide area networks (WANs) or any combinationthereof.

In the example of FIG. 16, the computing device 1600 comprises one ormore processor circuits or processing units 1602, one or more memorycircuits and/or storage circuit component(s) 1604 and one or moreinput/output (I/O) circuit devices 1606. Additionally, the computingdevice 1600 comprises a bus 1608 that allows the various circuitcomponents and devices to communicate with one another. The bus 1608represents one or more of any of several types of bus structures,including a memory bus or memory controller, a peripheral bus, anaccelerated graphics port, and a processor or local bus using any of avariety of bus architectures. The bus 1608 may comprise wired and/orwireless buses. The processing unit 1602 may be responsible forexecuting various software programs such as system programs,applications programs, and/or program modules/blocks to providecomputing and processing operations for the computing device 1600. Theprocessing unit 1602 may be responsible for performing various voice anddata communications operations for the computing device 1600 such astransmitting and receiving voice and data information over one or morewired or wireless communications channels. Although the processing unit1602 of the computing device 1600 is shown in the context of a singleprocessor architecture, it may be appreciated that the computing device1600 may use any suitable processor architecture and/or any suitablenumber of processors in accordance with the described embodiments. Inone embodiment, the processing unit 1602 may be implemented using asingle integrated processor. The processing unit 1602 may be implementedas a host central processing unit (CPU) using any suitable processorcircuit or logic device (circuit), such as a as a general purposeprocessor. The processing unit 1602 also may be implemented as a chipmultiprocessor (CMP), dedicated processor, embedded processor, mediaprocessor, input/output (I/O) processor, co-processor, microprocessor,controller, microcontroller, application specific integrated circuit(ASIC), field programmable gate array (FPGA), programmable logic device(PLD), or other processing device in accordance with the describedembodiments.

As shown, the processing unit 1602 may be coupled to the memory and/orstorage component(s) 1604 through the bus 1608. The bus 1608 maycomprise any suitable interface and/or bus architecture for allowing theprocessing unit 1602 to access the memory and/or storage component(s)1604. Although the memory and/or storage component(s) 1604 may be shownas being separate from the processing unit 1602 for purposes ofillustration, it is worthy to note that in various embodiments someportion or the entire memory and/or storage component(s) 1604 may beincluded on the same integrated circuit as the processing unit 1602.Alternatively, some portion or the entire memory and/or storagecomponent(s) 1604 may be disposed on an integrated circuit or othermedium (e.g., hard disk drive) external to the integrated circuit of theprocessing unit 1602. In various embodiments, the computing device 1600may comprise an expansion slot to support a multimedia and/or memorycard, for example. The memory and/or storage component(s) 1604 representone or more computer-readable media. The memory and/or storagecomponent(s) 1604 may be implemented using any computer-readable mediacapable of storing data such as volatile or non-volatile memory,removable or non-removable memory, erasable or non-erasable memory,writeable or re-writeable memory, and so forth. The memory and/orstorage component(s) 1604 may comprise volatile media (e.g., randomaccess memory (RAM)) and/or nonvolatile media (e.g., read only memory(ROM), Flash memory, optical disks, magnetic disks and the like). Thememory and/or storage component(s) 1604 may comprise fixed media (e.g.,RAM, ROM, a fixed hard drive, etc.) as well as removable media (e.g., aFlash memory drive, a removable hard drive, an optical disk). Examplesof computer-readable storage media may include, without limitation, RAM,dynamic RAM (DRAM), Double-Data-Rate DRAM (DDRAM), synchronous DRAM(SDRAM), static RAM (SRAM), read-only memory (ROM), programmable ROM(PROM), erasable programmable ROM (EPROM), electrically erasableprogrammable ROM (EEPROM), flash memory (e.g., NOR or NAND flashmemory), content addressable memory (CAM), polymer memory (e.g.,ferroelectric polymer memory), phase-change memory, ovonic memory,ferroelectric memory, silicon-oxide-nitride-oxide-silicon (SONOS)memory, magnetic or optical cards, or any other type of media suitablefor storing information.

The one or more I/O devices 1606 allow a user to enter commands andinformation to the computing device 1600, and also allow information tobe presented to the user and/or other components or devices. Examples ofinput devices include data ports, analog to digital converters (ADCs),digital to analog converters (DACs), a keyboard, a cursor control device(e.g., a mouse), a microphone, a scanner and the like. Examples ofoutput devices include data ports, ADC's, DAC's, a display device (e.g.,a monitor or projector, speakers, a printer, a network card). Thecomputing device 1600 may comprise an alphanumeric keypad coupled to theprocessing unit 1602. The keypad may comprise, for example, a QWERTY keylayout and an integrated number dial pad. The computing device 1600 maycomprise a display coupled to the processing unit 1602. The display maycomprise any suitable visual interface for displaying content to a userof the computing device 1600. In one embodiment, for example, thedisplay may be implemented by a liquid crystal display (LCD) such as atouch-sensitive color (e.g., 76-bit color) thin-film transistor (TFT)LCD screen. The touch-sensitive LCD may be used with a stylus and/or ahandwriting recognizer program.

The processing unit 1602 may be arranged to provide processing orcomputing resources to the computing device 1600. For example, theprocessing unit 1602 may be responsible for executing various softwareprograms including system programs such as operating system (OS) andapplication programs. System programs generally may assist in therunning of the computing device 1600 and may be directly responsible forcontrolling, integrating, and managing the individual hardwarecomponents of the computer system. The OS may be implemented, forexample, as a Microsoft® Windows OS, Symbian OS™, Embedix OS, Linux OS,Binary Run-time Environment for Wireless (BREW) OS, JavaOS, or othersuitable OS in accordance with the described embodiments. The computingdevice 1600 may comprise other system programs such as device drivers,programming tools, utility programs, software libraries, applicationprogramming interfaces (APIs), and so forth.

In various embodiments disclosed herein, a single component may bereplaced by multiple components and multiple components may be replacedby a single component to perform a given function or functions. Exceptwhere such substitution would not be operative, such substitution iswithin the intended scope of the embodiments.

I claim:
 1. An adaptive communication receiver for the demodulation anddetection of digitally modulated signals received over wirelesscommunication channels exhibiting multipath and fading, the receivercomprised of: an RF front end; an RF to complex baseband converter; aband limiting matched filter; a channel gain normalizer comprised of achannel signal power estimator, a channel gain estimator, and aparameter αestimator for providing the normalized channel output; ablind mode adaptive equalizer with hierarchical structure (BMAEHS)comprised of a level 1 adaptive system and a level 2 adaptive system forthe equalization of the normalized channel output wherein the level 2adaptive system is further comprised of a channel estimator and a modelerror correction signal generator; an initial data segment recoverycircuit comprised of a fixed equalizer for recovery of the data symbolsreceived during the initial convergence period of the BMAEHS; adifferential decoder; a complex baseband to data bit mapper; and anerror correction code decoder and de-interleaver.
 2. An adaptive digitalbeam former system for the demodulation and detection of digitallymodulated signals in blind mode received over an antenna array of Nelements, the system comprised of: an RF front end for each of the Narray elements; an RF to complex baseband converter for each of the Narray elements; a weighted signal combiner with adaptive weights; acombiner gain normalizer comprised of a channel signal power estimator,a channel gain estimator and a parameter α estimator for providing thenormalized output signal; a decision device; and a multilevel adaptationsubsystem for the adaptation of the combiner weights comprised of afirst correction signal vector generator for minimizing the errorbetween the input and output of the decision device, a second correctionsignal vector generator for minimizing the model error, and a thirdcorrection signal vector generator for maximizing the signal to noisepower ratio at the combiner output.
 3. A receiver method comprised ofreceiving an input signal by an RF front end; and a computer-implementedmethod for adaptive demodulation and detection of digitally modulatedsignals received over wireless communication channels exhibitingmultipath and fading, the computer-implemented method further comprisedof: conversion to baseband by an RF to complex baseband converterimplemented by a computer device, wherein the computer device comprisesat least one processor and associated memory; band limiting matchedfiltering by the computer device; implementing by the computer device achannel gain normalizer comprised of a channel signal power estimator, achannel gain estimator, and a parameter cc estimator for providing thenormalized channel output; implementing by the computer device a blindmode adaptive equalizer with hierarchical structure (BMAEHS) comprisedof a level 1 adaptive system and a level 2 adaptive system for theequalization of the normalized channel output wherein the level 2adaptive system is further comprised of a channel estimator and a modelerror correction signal generator; initial implementing, by the computerdevice, an initial data segment recovery circuit comprised of a fixedequalizer for recovery of the data symbols received during the initialconvergence period of the BMAEHS; differential decoding, by the computerdevice; complex baseband to data bit mapping, by the computer device;and error correction code decoding and de-interleaving, implemented bythe computer device providing the detected information data at theoutput of the computer device.
 4. An adaptive digital beam former methodcomprised of receiving RF source signal by an antenna array of Nelements, N RF front end receiver blocks and a computer-implementedmethod for the demodulation and detection of digitally modulated signalsin blind mode, the method comprised of: conversion to N baseband signalsby N RF to complex baseband converters implemented by a computer device;combining N complex baseband signals by a combiner with adaptive weightsimplemented by a computer device; implementing by a computer device acombiner gain normalizer comprised of a channel signal power estimator,a channel gain estimator and a parameter α estimator for providingnormalized signal output; detection of the data symbols with decisiondevice implemented by a computer device; and implementing by a computerdevice a multilevel adaptation subsystem for the adaptation of thecombiner weights comprised of a first correction signal vector generatorfor minimizing the error between the input and output of the decisiondevice, a second correction signal vector generator for minimizing themodel error, and a third correction signal vector generator formaximizing the signal to noise power ratio at the combiner output.